**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**6649

# Search results for: positive linear systems

##### 6649 Stability of a Special Class of Switched Positive Systems

**Authors:**
Xiuyong Ding,
Lan Shu,
Xiu Liu

**Abstract:**

This paper is concerned with the existence of a linear copositive Lyapunov function(LCLF) for a special class of switched positive linear systems(SPLSs) composed of continuousand discrete-time subsystems. Firstly, by using system matrices, we construct a special kind of matrices in appropriate manner. Secondly, our results reveal that the Hurwitz stability of these matrices is equivalent to the existence of a common LCLF for arbitrary finite sets composed of continuous- and discrete-time positive linear timeinvariant( LTI) systems. Finally, a simple example is provided to illustrate the implication of our results.

**Keywords:**
Linear co-positive Lyapunov functions,
positive systems,
switched systems.

##### 6648 On General Stability for Switched Positive Linear Systems with Bounded Time-varying Delays

**Authors:**
Xiu Liu,
Shouming Zhong,
Xiuyong Ding

**Abstract:**

This paper focuses on the problem of a common linear copositive Lyapunov function(CLCLF) existence for discrete-time switched positive linear systems(SPLSs) with bounded time-varying delays. In particular, applying system matrices, a special class of matrices are constructed in an appropriate manner. Our results reveal that the existence of a common copositive Lyapunov function can be related to the Schur stability of such matrices. A simple example is provided to illustrate the implication of our results.

**Keywords:**
Common linear co-positive Lyapunov functions,
positive systems,
switched systems,
delays.

##### 6647 Controller Synthesis of Switched Positive Systems with Bounded Time-Varying Delays

**Authors:**
Xinhui Wang,
Xiuyong Ding

**Abstract:**

This paper addresses the controller synthesis problem of discrete-time switched positive systems with bounded time-varying delays. Based on the switched copositive Lyapunov function approach, some necessary and sufficient conditions for the existence of state-feedback controller are presented as a set of linear programming and linear matrix inequality problems, hence easy to be verified. Another advantage is that the state-feedback law is independent on time-varying delays and initial conditions. A numerical example is provided to illustrate the effectiveness and feasibility of the developed controller.

**Keywords:**
Switched copositive Lyapunov functions,
positive linear systems,
switched systems,
time-varying delays,
stabilization.

##### 6646 A Spectral Decomposition Method for Ordinary Differential Equation Systems with Constant or Linear Right Hand Sides

**Authors:**
R. B. Ogunrinde,
C. C. Jibunoh

**Abstract:**

**Keywords:**
Spectral decomposition,
eigenvalues of the Jacobian,
linear RHS,
homogeneous linear systems.

##### 6645 On the Algorithmic Iterative Solutions of Conjugate Gradient, Gauss-Seidel and Jacobi Methods for Solving Systems of Linear Equations

**Authors:**
H. D. Ibrahim,
H. C. Chinwenyi,
H. N. Ude

**Abstract:**

In this paper, efforts were made to examine and compare the algorithmic iterative solutions of conjugate gradient method as against other methods such as Gauss-Seidel and Jacobi approaches for solving systems of linear equations of the form Ax = b, where A is a real n x n symmetric and positive definite matrix. We performed algorithmic iterative steps and obtained analytical solutions of a typical 3 x 3 symmetric and positive definite matrix using the three methods described in this paper (Gauss-Seidel, Jacobi and Conjugate Gradient methods) respectively. From the results obtained, we discovered that the Conjugate Gradient method converges faster to exact solutions in fewer iterative steps than the two other methods which took much iteration, much time and kept tending to the exact solutions.

**Keywords:**
conjugate gradient,
linear equations,
symmetric and positive definite matrix,
Gauss-Seidel,
Jacobi,
algorithm

##### 6644 Density Estimation using Generalized Linear Model and a Linear Combination of Gaussians

**Authors:**
Aly Farag,
Ayman El-Baz,
Refaat Mohamed

**Abstract:**

In this paper we present a novel approach for density estimation. The proposed approach is based on using the logistic regression model to get initial density estimation for the given empirical density. The empirical data does not exactly follow the logistic regression model, so, there will be a deviation between the empirical density and the density estimated using logistic regression model. This deviation may be positive and/or negative. In this paper we use a linear combination of Gaussian (LCG) with positive and negative components as a model for this deviation. Also, we will use the expectation maximization (EM) algorithm to estimate the parameters of LCG. Experiments on real images demonstrate the accuracy of our approach.

**Keywords:**
Logistic regression model,
Expectationmaximization,
Segmentation.

##### 6643 Delay-independent Stabilization of Linear Systems with Multiple Time-delays

**Authors:**
Ping He,
Heng-You Lan,
Gong-Quan Tan

**Abstract:**

**Keywords:**
Linear system,
Delay-independent stabilization,
Lyapunovfunctional,
Riccati algebra matrix equation.

##### 6642 A Note on the Convergence of the Generalized AOR Iterative Method for Linear Systems

**Authors:**
Zhong-xi Gao,
Hou-biao Li

**Abstract:**

Recently, some convergent results of the generalized AOR iterative (GAOR) method for solving linear systems with strictly diagonally dominant matrices are presented in [Darvishi, M.T., Hessari, P.: On convergence of the generalized AOR method for linear systems with diagonally dominant cofficient matrices. Appl. Math. Comput. 176, 128-133 (2006)] and [Tian, G.X., Huang, T.Z., Cui, S.Y.: Convergence of generalized AOR iterative method for linear systems with strictly diagonally dominant cofficient matrices. J. Comp. Appl. Math. 213, 240-247 (2008)]. In this paper, we give the convergence of the GAOR method for linear systems with strictly doubly diagonally dominant matrix, which improves these corresponding results.

**Keywords:**
Diagonally dominant matrix,
GAOR method,
Linear
system,
Convergence

##### 6641 Some Results on Parallel Alternating Two-stage Methods

**Authors:**
Guangbin Wang,
Xue Li

**Abstract:**

**Keywords:**
alternating two-stage,
convergence,
linear system,
parallel.

##### 6640 Jacobi-Based Methods in Solving Fuzzy Linear Systems

**Authors:**
Lazim Abdullah,
Nurhakimah Ab. Rahman

**Abstract:**

Linear systems are widely used in many fields of science and engineering. In many applications, at least some of the parameters of the system are represented by fuzzy rather than crisp numbers. Therefore it is important to perform numerical algorithms or procedures that would treat general fuzzy linear systems and solve them using iterative methods. This paper aims are to solve fuzzy linear systems using four types of Jacobi based iterative methods. Four iterative methods based on Jacobi are used for solving a general n × n fuzzy system of linear equations of the form Ax = b , where A is a crisp matrix and b an arbitrary fuzzy vector. The Jacobi, Jacobi Over-Relaxation, Refinement of Jacobi and Refinement of Jacobi Over-Relaxation methods was tested to a five by five fuzzy linear system. It is found that all the tested methods were iterated differently. Due to the effect of extrapolation parameters and the refinement, the Refinement of Jacobi Over-Relaxation method was outperformed the other three methods.

**Keywords:**
Fuzzy linear systems,
Jacobi,
Jacobi Over-
Relaxation,
Refinement of Jacobi,
Refinement of Jacobi Over-
Relaxation.

##### 6639 Block Homotopy Perturbation Method for Solving Fuzzy Linear Systems

**Authors:**
Shu-Xin Miao

**Abstract:**

In this paper, we present an efficient numerical algorithm, namely block homotopy perturbation method, for solving fuzzy linear systems based on homotopy perturbation method. Some numerical examples are given to show the efficiency of the algorithm.

**Keywords:**
Homotopy perturbation method,
fuzzy linear systems,
block linear system,
fuzzy solution,
embedding parameter.

##### 6638 Stability of Discrete Linear Systems with Periodic Coefficients under Parametric Perturbations

**Authors:**
Adam Czornik,
Aleksander Nawrat

**Abstract:**

**Keywords:**
Exponential stability,
time-varying linear systems,
periodic systems.

##### 6637 A Comparison of the Sum of Squares in Linear and Partial Linear Regression Models

**Authors:**
Dursun Aydın

**Abstract:**

**Keywords:**
Partial Linear Regression Model,
Linear RegressionModel,
Residuals,
Deviance,
Smoothing Spline.

##### 6636 Switching Rule for the Exponential Stability and Stabilization of Switched Linear Systems with Interval Time-varying Delays

**Authors:**
Kreangkri Ratchagit

**Abstract:**

This paper is concerned with exponential stability and stabilization of switched linear systems with interval time-varying delays. The time delay is any continuous function belonging to a given interval, in which the lower bound of delay is not restricted to zero. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton-s formula, a switching rule for the exponential stability and stabilization of switched linear systems with interval time-varying delays and new delay-dependent sufficient conditions for the exponential stability and stabilization of the systems are first established in terms of LMIs. Numerical examples are included to illustrate the effectiveness of the results.

**Keywords:**
Switching design,
exponential stability and stabilization,
switched linear systems,
interval delay,
Lyapunov function,
linear matrix inequalities.

##### 6635 Design of Nonlinear Observer by Using Augmented Linear System based on Formal Linearization of Polynomial Type

**Authors:**
Kazuo Komatsu,
Hitoshi Takata

**Abstract:**

The objective of this study is to propose an observer design for nonlinear systems by using an augmented linear system derived by application of a formal linearization method. A given nonlinear differential equation is linearized by the formal linearization method which is based on Taylor expansion considering up to the higher order terms, and a measurement equation is transformed into an augmented linear one. To this augmented dimensional linear system, a linear estimation theory is applied and a nonlinear observer is derived. As an application of this method, an estimation problem of transient state of electric power systems is studied, and its numerical experiments indicate that this observer design shows remarkable performances for nonlinear systems.

**Keywords:**
nonlinear system,
augmented linear system,
nonlinear observer,
formal linearization,
electric power system.

##### 6634 State Feedback Controller Design via Takagi- Sugeno Fuzzy Model: LMI Approach

**Authors:**
F. Khaber,
K. Zehar,
A. Hamzaoui

**Abstract:**

In this paper, we introduce a robust state feedback controller design using Linear Matrix Inequalities (LMIs) and guaranteed cost approach for Takagi-Sugeno fuzzy systems. The purpose on this work is to establish a systematic method to design controllers for a class of uncertain linear and non linear systems. Our approach utilizes a certain type of fuzzy systems that are based on Takagi-Sugeno (T-S) fuzzy models to approximate nonlinear systems. We use a robust control methodology to design controllers. This method not only guarantees stability, but also minimizes an upper bound on a linear quadratic performance measure. A simulation example is presented to show the effectiveness of this method.

**Keywords:**
Takagi-Sugeno fuzzy model,
state feedback,
linear matrix inequalities,
robust stability.

##### 6633 Numerical Solving of General Fuzzy Linear Systems by Huang's Method

**Authors:**
S. J. Hosseini Ghoncheh,
M. Paripour

**Abstract:**

In this paper the Huang-s method for solving a m×n fuzzy linear system when, m≤ n, is considered. The method in detail is discussed and illustrated by solving some numerical examples.

**Keywords:**
Fuzzy number,
fuzzy linear systems,
Huang's method.

##### 6632 Parallel Multisplitting Methods for Singular Linear Systems

**Authors:**
Guangbin Wang,
Fuping Tan

**Abstract:**

In this paper, we discuss convergence of the extrapolated iterative methods for linear systems with the coefficient matrices are singular H-matrices. And we present the sufficient and necessary conditions for convergence of the extrapolated iterative methods. Moreover, we apply the results to the GMAOR methods. Finally, we give one numerical example.

**Keywords:**
Singular H-matrix,
linear systems,
extrapolated iterative method,
GMAOR method,
convergence.

##### 6631 A Method for Quality Inspection of Motors by Detecting Abnormal Sound

**Authors:**
Tadatsugu Kitamoto

**Abstract:**

**Keywords:**
Acoustical diagnosis,
Neural networks,
K-means,
Short-time Fourier transformation

##### 6630 Simplex Method for Fuzzy Variable Linear Programming Problems

**Authors:**
S.H. Nasseri,
E. Ardil

**Abstract:**

Fuzzy linear programming is an application of fuzzy set theory in linear decision making problems and most of these problems are related to linear programming with fuzzy variables. A convenient method for solving these problems is based on using of auxiliary problem. In this paper a new method for solving fuzzy variable linear programming problems directly using linear ranking functions is proposed. This method uses simplex tableau which is used for solving linear programming problems in crisp environment before.

**Keywords:**
Fuzzy variable linear programming,
fuzzy number,
ranking function,
simplex method.

##### 6629 Online Robust Model Predictive Control for Linear Fractional Transformation Systems Using Linear Matrix Inequalities

**Authors:**
Peyman Sindareh Esfahani,
Jeffery Kurt Pieper

**Abstract:**

In this paper, the problem of robust model predictive control (MPC) for discrete-time linear systems in linear fractional transformation form with structured uncertainty and norm-bounded disturbance is investigated. The problem of minimization of the cost function for MPC design is converted to minimization of the worst case of the cost function. Then, this problem is reduced to minimization of an upper bound of the cost function subject to a terminal inequality satisfying the *l*_{2}-norm of the closed loop system. The characteristic of the linear fractional transformation system is taken into account, and by using some mathematical tools, the robust predictive controller design problem is turned into a linear matrix inequality minimization problem. Afterwards, a formulation which includes an integrator to improve the performance of the proposed robust model predictive controller in steady state condition is studied. The validity of the approaches is illustrated through a robust control benchmark problem.

**Keywords:**
Linear fractional transformation,
linear matrix inequality,
robust model predictive control,
state feedback control.

##### 6628 LMI Approach to Regularization and Stabilization of Linear Singular Systems: The Discrete-time Case

**Authors:**
Salim Ibrir

**Abstract:**

Sufficient linear matrix inequalities (LMI) conditions for regularization of discrete-time singular systems are given. Then a new class of regularizing stabilizing controllers is discussed. The proposed controllers are the sum of predictive and memoryless state feedbacks. The predictive controller aims to regularizing the singular system while the memoryless state feedback is designed to stabilize the resulting regularized system. A systematic procedure is given to calculate the controller gains through linear matrix inequalities.

**Keywords:**
Singular systems,
Discrete-time systems,
Regularization,
LMIs

##### 6627 Solving Fully Fuzzy Linear Systems by use of a Certain Decomposition of the Coefficient Matrix

**Authors:**
S. H. Nasseri,
M. Sohrabi,
E. Ardil

**Abstract:**

**Keywords:**
Fully fuzzy linear system,
Fuzzy number,
LUdecomposition.

##### 6626 Laplace Transformation on Ordered Linear Space of Generalized Functions

**Authors:**
K. V. Geetha,
N. R. Mangalambal

**Abstract:**

**Keywords:**
Laplace transformable generalized function,
positive cone,
topology of bounded convergence

##### 6625 On the Solution of Fully Fuzzy Linear Systems

**Authors:**
Hsuan-Ku Liu

**Abstract:**

A linear system is called a fully fuzzy linear system (FFLS) if quantities in this system are all fuzzy numbers. For the FFLS, we investigate its solution and develop a new approximate method for solving the FFLS. Observing the numerical results, we find that our method is accurate than the iterative Jacobi and Gauss- Seidel methods on approximating the solution of FFLS.

**Keywords:**
Fully fuzzy linear equations,
iterative method,
homotopy perturbation method,
approximate solutions.

##### 6624 TS Fuzzy Controller to Stochastic Systems

**Authors:**
Joabe Silva,
Ginalber Serra

**Abstract:**

**Keywords:**
Fuzzy Systems; Robust Stability,
Stochastic Control,
Stochastic Process

##### 6623 Recognition and Reconstruction of Partially Occluded Objects

**Authors:**
Michela Lecca,
Stefano Messelodi

**Abstract:**

A new automatic system for the recognition and re¬construction of resealed and/or rotated partially occluded objects is presented. The objects to be recognized are described by 2D views and each view is occluded by several half-planes. The whole object views and their visible parts (linear cuts) are then stored in a database. To establish if a region R of an input image represents an object possibly occluded, the system generates a set of linear cuts of R and compare them with the elements in the database. Each linear cut of R is associated to the most similar database linear cut. R is recognized as an instance of the object 0 if the majority of the linear cuts of R are associated to a linear cut of views of 0. In the case of recognition, the system reconstructs the occluded part of R and determines the scale factor and the orientation in the image plane of the recognized object view. The system has been tested on two different datasets of objects, showing good performance both in terms of recognition and reconstruction accuracy.

**Keywords:**
Occluded Object Recognition,
Shape Reconstruction,
Automatic Self-Adaptive Systems,
Linear Cut.

##### 6622 Numerical Simulations on Feasibility of Stochastic Model Predictive Control for Linear Discrete-Time Systems with Random Dither Quantization

**Authors:**
Taiki Baba,
Tomoaki Hashimoto

**Abstract:**

**Keywords:**
Model predictive control,
stochastic systems,
probabilistic constraints,
random dither quantization.

##### 6621 Bi-linear Complementarity Problem

**Authors:**
Chao Wang,
Ting-Zhu Huang Chen Jia

**Abstract:**

In this paper, we propose a new linear complementarity problem named as bi-linear complementarity problem (BLCP) and the method for solving BLCP. In addition, the algorithm for error estimation of BLCP is also given. Numerical experiments show that the algorithm is efficient.

**Keywords:**
Bi-linear complementarity problem,
Linear complementarity
problem,
Extended linear complementarity problem,
Error
estimation,
P-matrix,
M-matrix.

##### 6620 Preconditioned Jacobi Method for Fuzzy Linear Systems

**Authors:**
Lina Yan,
Shiheng Wang,
Ke Wang

**Abstract:**

A preconditioned Jacobi (PJ) method is provided for solving fuzzy linear systems whose coefficient matrices are crisp Mmatrices and the right-hand side columns are arbitrary fuzzy number vectors. The iterative algorithm is given for the preconditioned Jacobi method. The convergence is analyzed with convergence theorems. Numerical examples are given to illustrate the procedure and show the effectiveness and efficiency of the method.

**Keywords:**
preconditioning,
M-matrix,
Jacobi method,
fuzzy linear
system (FLS).