On stability and performance analysis of discrete-time piecewise affine systems

This paper considers exponential stability and quadratic performance of discrete-time piecewise affine systems. We propose a procedure to obtain an increasing sequence of state-space partitions, and show that, whenever the procedure terminates after a finite number of steps, a nonconservative stability and performance analysis is achieved by solving a finite number of linear matrix inequalities. The result is illustrated via numerical examples, which include a model of the PWM DC-DC power converter.

[1]  R. Sanfelice,et al.  Hybrid dynamical systems , 2009, IEEE Control Systems.

[2]  Stefan Almér,et al.  Stability Analysis of a Class of PWM Systems , 2007, IEEE Transactions on Automatic Control.

[3]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[4]  M. Branicky.  Multiple Lyapunov functions and other analysis tools for switched and hybrid systems , 1998, IEEE Trans. Autom. Control..

[5]  M. Johansson,et al.  Piecewise Linear Control Systems , 2003 .

[6]  Geir E. Dullerud,et al.  LMI tools for eventually periodic systems , 2002, Syst. Control. Lett..

[7]  Sanam Mirzazad-Barijough,et al.  On stability characterization of discrete-time piecewise linear systems , 2010, Proceedings of the 2010 American Control Conference.

[8]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[9]  R. Decarlo,et al.  Perspectives and results on the stability and stabilizability of hybrid systems , 2000, Proceedings of the IEEE.

[10]  Anders Rantzer,et al.  Computation of piecewise quadratic Lyapunov functions for hybrid systems , 1997, 1997 European Control Conference (ECC).

[11]  A.R. Teel,et al.  Hybrid Dynamical Systems: Robust Stability and Control , 2006, 2007 Chinese Control Conference.

[12]  Ji-Woong Lee.  Separation in Stability Analysis of Piecewise Linear Systems in Discrete Time , 2008, HSCC.

[13]  Geir E. Dullerud,et al.  Uniformly Stabilizing Sets of Switching Sequences for Switched Linear Systems , 2007, IEEE Transactions on Automatic Control.

[14]  Manfred Morari,et al.  Analysis of discrete-time piecewise affine and hybrid systems , 2002, Autom..

[15]  Thomas A. Henzinger,et al.  Hybrid Automata: An Algorithmic Approach to the Specification and Verification of Hybrid Systems , 1992, Hybrid Systems.

[16]  John N. Tsitsiklis,et al.  Complexity of stability and controllability of elementary hybrid systems , 1999, Autom..

[17]  Ji-Woong Lee,et al.  A computational stability analysis of discrete-time piecewise linear systems , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.