Stability of uncertain piecewise affine systems with time-delay

This paper addresses the problem of robust stability of piecewise affine (PWA) uncertain systems with unknown time-varying delay in the state. It is assumed that the uncertainty is norm-bounded and that upper bounds on the state delay and its rate of change are available. A set of linear matrix inequalities (LMI) is derived providing sufficient conditions for the stability of the system. These conditions depend on the upper bound of the delay. The main contributions of the paper are as follows. First, new delay-dependent LMI conditions are derived for the stability of PWA time-delay systems. Second, the stability conditions are extended to the case of uncertain PWA time-delay systems. Numerical examples are presented to show the effectiveness of the approach.

[1]  Luis Rodrigues.  Stability analysis of piecewise-affine systems using controlled invariant sets , 2004, Syst. Control. Lett..

[2]  Shahin Hashtrudi-Zad,et al.  Supervisory control of switching control systems , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[3]  Stephen P. Boyd,et al.  Piecewise-affine state feedback for piecewise-affine slab systems using convex optimization , 2005, Syst. Control. Lett..

[4]  Edward J. Davison,et al.  Pseudo-decentralized switching control , 2003, Autom..

[5]  Juing-Huei Su.  Further results on the robust stability of linear systems with a single time delay , 1994 .

[6]  Gene F. Franklin,et al.  Feedback Control of Dynamic Systems , 1986 .

[7]  A.G. Beccuti,et al.  Optimal Control of the Boost dc-dc Converter , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[8]  Bingyong Tang,et al.  A linear matrix inequality approach for robust control of systems with delayed states , 2000, Eur. J. Oper. Res..

[9]  Wei Zhang,et al.  Stability of networked control systems , 2001 .

[10]  J. Imura,et al.  Optimal control of sampled-data piecewise affine systems and its application to CPU processing control , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[11]  Stephen P. Boyd,et al.  Quadratic stabilization and control of piecewise-linear systems , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[12]  Rein Luus,et al.  Piecewise linear control , 2000, Iterative Dynamic Programming.

[13]  M. Parlakçi.  Robust stability of uncertain time-varying state-delayed systems , 2006 .

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

[15]  Jonathan P. How,et al.  Toward unified analysis and controller synthesis for a class of hybrid systems , 2006 .

[16]  Amir G. Aghdam,et al.  An adaptive tracking problem for a family of retarded time‐delay plants , 2007 .

[17]  J. How,et al.  Observer-based control of piecewise-affine systems , 2003 .

[18]  El Kebir Boukas,et al.  Piecewise-linear Hinfinity controller synthesis with applications to inventory control of switched production systems , 2006, Autom..

[19]  Stéphane Bibian,et al.  Time delay compensation of digital control for DC switchmode power supplies using prediction techniques , 2000 .

[20]  Long Wang,et al.  Stability of switched systems with time-varying delays: delay-dependent common Lyapunov functional approach , 2006, 2006 American Control Conference.

[21]  Kemin Zhou,et al.  Robust stability of uncertain time-delay systems , 2000, IEEE Trans. Autom. Control..

[22]  Lihua Xie,et al.  Robust control of a class of uncertain nonlinear systems , 1992 .

[23]  Emilia Fridman,et al.  Parameter dependent stability and stabilization of uncertain time-delay systems , 2003, IEEE Trans. Autom. Control..

[24]  Edward J. Davison,et al.  Decentralized switching control for hierarchical systems , 2007, Autom..

[25]  M. Parlakçi,et al.  Robust stability of uncertain time-varying state-delayed systems , 2006, 2006 American Control Conference.

[26]  Vladimir L. Kharitonov,et al.  Exponential estimates for retarded time-delay systems: an LMI approach , 2005, IEEE Transactions on Automatic Control.

[27]  Tong Heng Lee,et al.  A less conservative robust stability test for linear uncertain time-delay systems , 2006, IEEE Trans. Autom. Control..

[28]  J. Hespanha,et al.  Piecewise quadratic Lyapunov functions for piecewise affine time-delay systems , 2004, Proceedings of the 2004 American Control Conference.

[29]  Jun Zhao,et al.  Stability and L2-gain analysis for switched delay systems: A delay-dependent method , 2006, Autom..

[30]  Qing-Long Han,et al.  On robust stability of time-delay systems with norm-bounded uncertainty , 2001, IEEE Trans. Autom. Control..

[31]  A. Michel,et al.  Stability and /spl Lscr//sub 2/ gain analysis for switched symmetric systems with time delay , 2003, Proceedings of the 2003 American Control Conference, 2003..

[32]  Erik I. Verriest,et al.  Frequency domain robust stability criteria for linear delay systems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.