Regional asymptotic stability analysis for discrete-time delayed systems with saturation nonlinearity

This paper presents a novel method for asymptotic stability analysis of discrete-time systems with state delay and saturation nonlinearity. Based on Lyapunov functional and LMI (linear matrix inequality) framework, new stability criteria are derived in terms of LMIs by using some properties of the saturation nonlinearity. The criteria can be applied to the global and regional stability. Numerical examples are given to verify the theoretical result of the proposed method.

[1]  Karolos M. Grigoriadis,et al.  A unified algebraic approach to linear control design , 1998 .

[2]  Luca Zaccarian,et al.  Piecewise-quadratic Lyapunov functions for systems with deadzones or saturations , 2009, Syst. Control. Lett..

[3]  Vladimir L. Kharitonov,et al.  Stability of Time-Delay Systems , 2003, Control Engineering.

[4]  Sophie Tarbouriech,et al.  LMI relaxations for robust stability of linear systems with saturating controls , 1999, Autom..

[5]  Jingcheng Wang,et al.  Invariant ellipsoids for single-input system with actuator saturation by employing output feedback , 2006, J. Frankl. Inst..

[6]  Shyh-Feng Chen.  Asymptotic stability of discrete-time systems with time-varying delay subject to saturation nonlinearities , 2009 .

[7]  C. Ibáñez,et al.  Controlling the inverted pendulum by means of a nested saturation function , 2008 .

[8]  Ahmad Haidar,et al.  Delay-range-dependent control synthesis for time-delay systems with actuator saturation , 2008, Autom..

[9]  Sophie Tarbouriech,et al.  Synthesis of controllers for continuous-time delay systems with saturating controls via LMIs , 2000, IEEE Trans. Autom. Control..

[10]  Vladimir A. Yakubovich,et al.  Linear Matrix Inequalities in System and Control Theory (S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan) , 1995, SIAM Rev..

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

[12]  Zongli Lin,et al.  Stability analysis of discrete-time systems with actuator saturation by a saturation-dependent Lyapunov function , 2003, Autom..

[13]  Shyh-Feng Chen,et al.  Delay-dependent stability for 2D systems with time-varying delay subject to state saturation in the Roesser model , 2010, Appl. Math. Comput..

[14]  Michel Verhaegen,et al.  Proceedings of the 37th IEEE Conference on Decision and Control , 1998 .

[15]  Masami Saeki,et al.  l/sub 2/-gain analysis of discrete-time systems with saturation nonlinearity using parameter dependent Lyapunov function , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[16]  V. Krishna Rao Kandanvli,et al.  Robust stability of discrete-time state-delayed systems employing generalized overflow nonlinearities , 2008 .

[17]  P. Olver.  Nonlinear Systems , 2013 .

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

[19]  Mohammad Shoeybi,et al.  Control of a Nonlinear System Using the Saturation Phenomenon , 2005 .

[20]  Stephen P. Boyd,et al.  Analysis of linear systems with saturation using convex optimization , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[21]  Tingshu Hu,et al.  Analysis and design for discrete-time linear systems subject to actuator saturation , 2002, Syst. Control. Lett..

[22]  Zongli Lin,et al.  Stability analysis of discrete-time systems with actuator saturation by a saturation-dependent Lyapunov function , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[23]  Jyh-Horng Chou.  Stabilization of linear discrete-time systems with actuator saturation , 1991 .