**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**31814

##### Robust Disturbance Rejection for Left Invertible Singular Systems with Nonlinear Uncertain Structure

**Authors:**
Fotis N. Koumboulis,
Michael G. Skarpetis,
Maria P. Tzamtzi

**Abstract:**

The problem of robust disturbance rejection (RDR) using a proportional state feedback controller is studied for the case of Left Invertible MIMO generalized state space linear systems with nonlinear uncertain structure. Sufficient conditions for the problem to have a solution are established. The set of all proportional feedback controllers solving the problem subject to these conditions is analytically determined.

**Keywords:**
System theory,
uncertain systems,
robust control,
singular systems.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1332746

**References:**

[1] F. N. Koumboulis, M.G. Skarpetis and M. P. Tzamtzi "Robust Input - Output decoupling for singular systems with nonlinear uncertain structure", Proceedings of the European Control Conference 2007, 2-5 July, 2007.

[2] W. M. Wonham and A. S. Morse, "Decoupling and Pole assignment in linear multivariable systems", SIAM J. Contr., vol. 8, pp. 1-18, 1970.

[3] V. Kucera, "Disturbance rejection: A polynomial approach", IEEE Trans. Automat. Contr., vol. 28, pp. 508-511, 1982.

[4] P. N. Paraskevopoulos, F. N. Koumboulis and K. G. Tzierakis, "Disturbance Rejection of Left invertible Systems", Automatica, vol. 28, pp. 427-430, 1992.

[5] P. N. Paraskevopoulos, F. N. Koumboulis and K. G. Tzierakis, "Disturbance rejection of left-invertible generalized state space systems", IEEE Trans. Automat. Contr., vol. 39, pp. 185-190, 1993.

[6] L. R. Fletcher and A. Aasarai, "On disturbance decoupling of descriptor systems", SIAM J. Contr. Optimiz., vol. 27, pp. 1319-1332, 1989.

[7] F. N. Koumboulis and K. G. Tzierakis, "Meeting Transfer Function Requirements via static measurement output feedback", J. of the Franklin Institute, vol. 335B, pp. 661-667, 1998.

[8] A. Ailon, "A solution to the disturbance decoupling problem in singular systems via analogy with state-space systems", Automatica, vol. 29, pp. 1541-1545, 1993.

[9] F. N. Koumboulis, and M. G. Skarpetis, "Robust Disturbance Rejection for Left-Invertible Linear Systems with Nonlinear-Uncertain Structure", ASME J. of Dynamic Systems, Measurement and Control, vol. 121, pp. 218-225, 1999.

[10] S. Bhattacharyya, A.C. del Nero Gomes and J.W. Houze, "The structure of robust disturbance rejection control", IEEE Trans. Automat. Contr., vol. 28, pp. 874-861, 1982.

[11] G. Conte and A.M. Perdon, "Robust disturbance decoupling problem for parameter dependent families of linear systems", Automatica, vol. 24, pp. 475-478, 1992.

[12] M. B. Estrada, and M. Malabre, "Structural conditions for disturbance decoupling with stability using proportional and derivative control laws" IEEE Trans. Automat. Contr., vol. 46, pp. 160-165, 2001.

[13] J. G. Owen and G. Zames, "Duality theory of robust disturbance attenuation", Automatica, vol. 29, pp. 695-705, 1992.

[14] G. Zames and J. G. Owen, "Duality Theory for MIMO robust disturbance rejection", IEEE Trans. Automat. Contr., vol. 38, pp. 743- 752, 1992.

[15] F. N. Koumboulis, M. G. Skarpetis and G. E. Panagiotakis, "Robust Disturbance Rejection via P-D State Feedback - Example for Lane Keeping of Highway Vehicles", Transactions of the Institute of Measurement & Control, vol. 28, pp. 141-143, 2006.

[16] F. N. Koumboulis, "Characterization of the allowable perturbations for disturbance rejection and data sensitivity", Proceedings of the 3rd IEEE International Conference on Electronics, Circuits, and Systems (ICECS 96), Rodos, Greece, vol. 1, pp. 479-482, 1996.

[17] F.N. Koumboulis and M.G. Skarpetis, "Robust Triangular Decoupling with Application to 4WS Cars", IEEE Transactions on Automatic Control, vol. 45, pp. 344-352, 2000.

[18] F.N. Koumboulis and M.G. Skarpetis, "Input output decoupling for systems with nonlinear uncertain structure", J. of the Franklin Institute: vol. 333(B), No. 4, pp. 593-624, 1996.