Efficient LMI-Based Quadratic Stabilization of Interval LPV Systems With Noisy Parameter Measures

The purpose of this note is to consider the quadratic stabilization of LPV systems in the realistic case where only Gaussian noisy parameter measures are available. Though neglected in the actual literature on LPV systems, this question is particular important because in all situations of a practical interest the parameter measurements (or estimates) are never exact. The assumed noisy nature of physical parameter readings requires a specifically developed approach consisting of mixed robust and LPV control methods. In the present case, an approach based on a vertex result on interval time varying (ITV) matrices is proposed. This allows the solvability conditions to be stated in terms of a set of LMI's, whose number is independent of the number of time-varying parameters.

[1]  Franco Blanchini,et al.  Stabilization of LPV systems: state feedback, state estimation and duality , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[2]  A. Packard,et al.  Robust performance of linear parametrically varying systems using parametrically-dependent linear feedback , 1994 .

[3]  Kamal Premaratne,et al.  Robust stability of time-variant interval matrices , 1990, 29th IEEE Conference on Decision and Control.

[4]  Panos J. AntsaklisDepartment.  Design of Output Feedback Controllers for Robust Stability and Optimal Performance of Discrete-Time Systems , 1994 .

[5]  Pierre Apkarian,et al.  Self-scheduled H∞ control of linear parameter-varying systems: a design example , 1995, Autom..

[6]  J. Bernussou,et al.  On Inexact LPV Control Design of Continuous–Time Polytopic Systems , 2008, IEEE Transactions on Automatic Control.

[7]  P. Gahinet,et al.  Affine parameter-dependent Lyapunov functions for real parametric uncertainty , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[8]  S. Rinaldi,et al.  Positive Linear Systems: Theory and Applications , 2000 .

[9]  Athanasios Sideris,et al.  H ∞ control with parametric Lyapunov functions , 1997 .

[10]  G. W. Stewart,et al.  Stochastic Perturbation Theory , 1990, SIAM Rev..

[11]  Jamal Daafouz,et al.  Parameter dependent Lyapunov functions for discrete time systems with time varying parametric uncertainties , 2001, Syst. Control. Lett..

[12]  C. Desoer,et al.  Feedback Systems: Input-Output Properties , 1975 .

[13]  Hoang Duong Tuan,et al.  Mixed H/sub 2//H/sub /spl infin// multi-channel linear parameter-varying control in discrete time , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[14]  Eugenius Kaszkurewicz,et al.  Robust stabilization of time-varying discrete interval systems , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[15]  P. Gahinet,et al.  Affine parameter-dependent Lyapunov functions and real parametric uncertainty , 1996, IEEE Trans. Autom. Control..

[16]  Fan Wang,et al.  Improved stability analysis and gain-scheduled controller synthesis for parameter-dependent systems , 2002, IEEE Trans. Autom. Control..

[17]  Pierre Apkarian,et al.  Advanced gain-scheduling techniques for uncertain systems , 1998, IEEE Trans. Control. Syst. Technol..

[18]  L. Jetto,et al.  Some remarks on the Schur stability of interval polynomials , 2008, 2008 16th Mediterranean Conference on Control and Automation.

[19]  P. Apkarian,et al.  Mixed H2/H∞ multi-channel linear parameter-varying control in discrete time , 2000 .

[20]  Valentina Orsini,et al.  Some remarks on the robust Schur stability analysis of interval polynomials , 2009, Int. J. Control.

[21]  Fen Wu,et al.  Gain-scheduling control of LFT systems using parameter-dependent Lyapunov functions , 2005, Proceedings of the 2005, American Control Conference, 2005..