Dynamic Anti-Windup Control Design for Markovian Jump Delayed Systems with Input Saturation

This paper deals with the problem of robust stabilization for Markovian jump delayed systems with partially known transition rates subject to input saturation. The problem we address is the design of dynamic anti-windup compensators, which guarantee that the resulting closed-loop constrained systems are robustly mean-square stable. By employing local sector conditions and an appropriate Lyapunov-Krasovskii function, some sufficient conditions for the solution to this problem are derived in terms of linear matrix inequalities. Finally, a numerical example is provided to demonstrate the effectiveness of proposed method.

[1]  Shengyuan Xu,et al.  Delay-Dependent $H_{\infty }$ Control and Filtering for Uncertain Markovian Jump Systems With Time-Varying Delays , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[2]  P. Shi,et al.  Robust Kalman Filter Design for Markovian Jump Linear Systems with Norm-Bounded Unknown Nonlinearities , 2005 .

[3]  Ligang Wu,et al.  A New Approach to Stability Analysis and Stabilization of Discrete-Time T-S Fuzzy Time-Varying Delay Systems , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[4]  Gin-Der Wu,et al.  A TS-Type Maximizing-Discriminability-Based Recurrent Fuzzy Network for Classification Problems , 2011, IEEE Transactions on Fuzzy Systems.

[5]  Manfred Morari,et al.  A unified framework for the study of anti-windup designs , 1994, Autom..

[6]  H. Su,et al.  Delay‐dependent H∞ control for singular Markovian jump systems with time delay , 2009 .

[7]  Shengyuan Xu,et al.  Passivity-based control for uncertain stochastic jumping systems with mode-dependent round-trip time delays , 2012, J. Frankl. Inst..

[8]  Huijun Gao,et al.  I filtering for 2D Markovian jump systems , 2008, Autom..

[9]  Victor Sreeram,et al.  Partially mode-dependent H∞ filtering for discrete-time Markovian jump systems with partly unknown transition probabilities , 2010, Signal Process..

[10]  Hamid Reza Karimi,et al.  Robust Delay-Dependent $H_{\infty}$ Control of Uncertain Time-Delay Systems With Mixed Neutral, Discrete, and Distributed Time-Delays and Markovian Switching Parameters , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[11]  Manfred Morari,et al.  Multiplier theory for stability analysis of anti-windup control systems , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[12]  Xudong Zhao,et al.  New robust delay-dependent stability and H∞ analysis for uncertain Markovian jump systems with time-varying delays , 2010, J. Frankl. Inst..

[13]  P. Shi,et al.  ℋ∞ Filter for Uncertain Markovian Jump Nonlinear Systems: An LMI Approach , 2007 .

[14]  Hamid Reza Karimi,et al.  New Delay-Dependent Exponential $H_{\infty}$ Synchronization for Uncertain Neural Networks With Mixed Time Delays , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[15]  Shengyuan Xu,et al.  Passivity-based Control for Markovian Jump Systems via Retarded Output Feedback , 2012, Circuits Syst. Signal Process..

[16]  El-Kébir Boukas,et al.  Free-Weighting Matrices Delay-Dependent Stabilization for Systems with Time-Varying Delays , 2007 .

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

[18]  Fuchun Sun,et al.  Controller design for Markov jumping systems subject to actuator saturation , 2006, Autom..

[19]  Yu Kang,et al.  Estimating the Delay-time for the Stability of Markovian Jump Bilinear Systems with Saturating Actuators: Estimating the Delay-time for the Stability of Markovian Jump Bilinear Systems with Saturating Actuators , 2010 .

[20]  Shengyuan Xu,et al.  Delay-dependent H∞ control for jumping delayed systems with two Markov processes , 2011 .

[21]  Huijun Gao,et al.  New Passivity Analysis for Neural Networks With Discrete and Distributed Delays , 2010, IEEE Transactions on Neural Networks.

[22]  Shengyuan Xu,et al.  On robust H∞ filtering of uncertain Markovian jump time‐delay systems , 2012 .

[23]  Yu Kang,et al.  Estimating the Delay-time for the Stability of Markovian Jump Bilinear Systems with Saturating Actuators , 2010 .

[24]  David G. Ward,et al.  Anti-windup design of output tracking systems subject to actuator saturation and constant disturbances , 2004, Autom..

[25]  Mayuresh V. Kothare,et al.  Simultaneous linear and anti-windup controller synthesis using multiobjective convex optimization , 2009, Autom..

[26]  Sheng Liu,et al.  Static Anti-windup Synthesis for a Class of Linear Systems Subject to Actuator Amplitude and Rate Saturation , 2009 .

[27]  Jie Zhang,et al.  Stabilization for Markovian jump systems with partial information on transition probability based on free-connection weighting matrices , 2011, Autom..

[28]  Huaguang Zhang,et al.  Optimal control laws for time-delay systems with saturating actuators based on heuristic dynamic programming , 2010, Neurocomputing.

[29]  Jin-Hua She,et al.  Delay-dependent exponential stability of delayed neural networks with time-varying delay , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[30]  R. Lu,et al.  Delay-dependent H∞ control for singular Markovian jump systems with time delay , 2013 .

[31]  Fei Liu,et al.  Controlling uncertain fuzzy neutral dynamic systems with Markov jumps , 2010 .

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

[33]  James Lam,et al.  Further Results on Exponential Estimates of Markovian Jump Systems With Mode-Dependent Time-Varying Delays , 2011, IEEE Transactions on Automatic Control.

[34]  Wei Xing Zheng,et al.  Passivity Analysis and Passification of Markovian Jump Systems , 2010, Circuits Syst. Signal Process..

[35]  Seong-Sik Yoon,et al.  Dynamic anti-windup scheme for feedback linearizable nonlinear control systems with saturating inputs , 2008, Autom..

[36]  Yongduan Song,et al.  A Novel Approach to Filter Design for T–S Fuzzy Discrete-Time Systems With Time-Varying Delay , 2012, IEEE Transactions on Fuzzy Systems.

[37]  Lihua Xie,et al.  Output feedback H∞ control of systems with parameter uncertainty , 1996 .

[38]  Shengyuan Xu,et al.  Fuzzy H ∞ filtering for nonlinear Markovian jump neutral systems , 2011, Int. J. Syst. Sci..

[39]  Jianbin Qiu,et al.  Model Approximation for Discrete-Time State-Delay Systems in the T–S Fuzzy Framework , 2011, IEEE Transactions on Fuzzy Systems.

[40]  Yang Tang,et al.  Synchronization of Stochastic Delayed Neural Networks with Markovian Switching and its Application , 2009, Int. J. Neural Syst..

[41]  Bing Chen,et al.  Robust Stability for Uncertain Delayed Fuzzy Hopfield Neural Networks With Markovian Jumping Parameters , 2009, IEEE Trans. Syst. Man Cybern. Part B.

[42]  Sheng Liu,et al.  Static Anti-windup Synthesis for a Class of Linear Systems Subject to Actuator Amplitude and Rate Saturation: Static Anti-windup Synthesis for a Class of Linear Systems Subject to Actuator Amplitude and Rate Saturation , 2009 .

[43]  Luca Zaccarian,et al.  L2 anti-windup for linear dead-time systems , 2005, Syst. Control. Lett..

[44]  Hamid Reza Karimi,et al.  A sliding mode approach to H∞ synchronization of master-slave time-delay systems with Markovian jumping parameters and nonlinear uncertainties , 2012, J. Frankl. Inst..

[45]  Wei Xing Zheng,et al.  Fault Detection Filter Design for Markovian Jump Singular Systems With Intermittent Measurements , 2011, IEEE Transactions on Signal Processing.

[46]  Peng Shi,et al.  Robust filtering for jumping systems with mode-dependent delays , 2006, Signal Process..