An anti-windup design to robust H∞ control for singular Markovian jump systems with actuator saturation and general unknown transition rates

Abstract This paper is concerned with the problem of robust H ∞ control for a class of singular Markovian jump systems (SMJSs) with generally uncertain transition rates (GUTRs) and actuator saturation via anti-windup design. In this GUTR model, each transition rate can be completely unknown or only its estimate value is known. Under the assumption that a set of linear dynamic output feedback controllers have been designed to stabilize the SMJSs in the absence of actuator saturation, anti-windup compensators are designed to impair the actuator saturation effect on the closed-loop systems subject to admissible external disturbances, Ito-type stochastic disturbances, transition rate and norm-bounded parameter uncertainties. Anti-windup compensation gains can be derived via solving a convex optimization problem with constraints of a set of linear matrix inequalities (LMIs). Finally, a numerical example is presented to illustrate the effectiveness and applicability of the proposed method.

[1]  Zongli Lin,et al.  Design of Saturation-Based Switching Anti-Windup Gains for the Enlargement of the Domain of Attraction , 2013, IEEE Transactions on Automatic Control.

[2]  Martin J. Hayes,et al.  Robust performance for an energy sensitive wireless body area network – an anti-windup approach , 2009, Int. J. Control.

[3]  Xuerong Mao,et al.  Stochastic Differential Equations With Markovian Switching , 2006 .

[4]  Yonggui Kao,et al.  Delay-Dependent Robust Exponential Stability of Impulsive Markovian Jumping Reaction-Diffusion Cohen-Grossberg Neural Networks , 2012, Neural Processing Letters.

[5]  Jianbin Qiu,et al.  Fuzzy-Model-Based Piecewise ${\mathscr H}_{\infty }$ Static-Output-Feedback Controller Design for Networked Nonlinear Systems , 2010, IEEE Transactions on Fuzzy Systems.

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

[7]  Guido Herrmann,et al.  A non-square sector condition and its application in deferred-action anti-windup compensator design , 2014, Autom..

[8]  Wei Xing Zheng,et al.  Anti-windup design of uncertain discrete-time Markovian jump systems with partially known transition probabilities and saturating actuator , 2015, Int. J. Syst. Sci..

[9]  Peng Shi,et al.  Transition probability bounds for the stochastic stability robustness of continuous- and discrete-time Markovian jump linear systems , 2006, Autom..

[10]  Jing Wang,et al.  Memory feedback controller design for stochastic Markov jump distributed delay systems with input saturation and partially known transition rates , 2015 .

[11]  Yonggui Kao,et al.  Stabilization of Singular Markovian Jump Systems With Generally Uncertain Transition Rates , 2014, IEEE Transactions on Automatic Control.

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

[13]  Lixian Zhang,et al.  Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities , 2009, Autom..

[14]  Jing Wang,et al.  Finite-time H∞ control for a class of Markovian jump delayed systems with input saturation , 2013 .

[15]  P. Daoutidis,et al.  An observer-based anti-windup scheme for non-linear systems with input constraints , 1999 .

[16]  Peng Shi,et al.  Asynchronous I2-I∞ filtering for discrete-time stochastic Markov jump systems with randomly occurred sensor nonlinearities , 2014, Autom..

[17]  B. Lohmann,et al.  H∞ control of parameter-dependent state-delayed systems using polynomial parameter-dependent quadratic functions , 2005 .

[18]  Lixian Zhang,et al.  Mode-dependent Hinfinity filtering for discrete-time Markovian jump linear systems with partly unknown transition probabilities , 2009, Autom..

[19]  Matthew C. Turner,et al.  Anti-windup synthesis for systems with rate-limits using Riccati equations , 2010, Int. J. Control.

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

[21]  Jun Zhao,et al.  L2-gain analysis and anti-windup design of discrete-time switched systems with actuator saturation , 2012, Int. J. Autom. Comput..

[22]  Luis C. Dias,et al.  Uncertainty and robustness in planning and decision-making , 2014, Int. J. Syst. Sci..

[23]  Hamid Reza Karimi,et al.  Local Capacity $H_{\infty}$ Control for Production Networks of Autonomous Work Systems With Time-Varying Delays , 2010, IEEE Transactions on Automation Science and Engineering.

[24]  Yonggui Kao,et al.  Stability in mean of partial variables for stochastic reaction-diffusion systems with Markovian switching , 2014, J. Frankl. Inst..

[25]  G. Song,et al.  Stability and l 2 -gain analysis for a class of discrete-time non-linear Markovian jump systems with actuator saturation and incomplete knowledge of transition probabilities , 2012 .

[26]  Yonggui Kao,et al.  Delay-dependent robust exponential stability of Markovian jumping reaction-diffusion Cohen-Grossberg neural networks with mixed delays , 2012, J. Frankl. Inst..

[27]  Jianbin Qiu,et al.  A New Design of Delay-Dependent Robust ${\cal H}_{\bm \infty}$ Filtering for Discrete-Time T--S Fuzzy Systems With Time-Varying Delay , 2009, IEEE Transactions on Fuzzy Systems.

[28]  Ye Zhao,et al.  Asynchronous Filtering of Discrete-Time Switched Linear Systems With Average Dwell Time , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[29]  S. Galeani,et al.  Non-linear anti-windup for manual flight control , 2005 .

[30]  Luca Zaccarian,et al.  A Benchmark Example for Anti-windup Synthesis in Active Vibration Isolation Tasks and an L2 Anti-windup Solution , 2000, Eur. J. Control.

[31]  James Lam,et al.  Analysis and Synthesis of Markov Jump Linear Systems With Time-Varying Delays and Partially Known Transition Probabilities , 2008, IEEE Transactions on Automatic Control.

[32]  Hamid Reza Karimi,et al.  Stability analysis and control synthesis of neutral systems with time-varying delays and nonlinear uncertainties , 2009 .

[33]  Wei Xing Zheng,et al.  Robust ℋ∞ filtering of Markovian jump stochastic systems with uncertain transition probabilities , 2011, Int. J. Syst. Sci..

[34]  James Lam,et al.  On robust stabilization of Markovian jump systems with uncertain switching probabilities , 2005, Autom..

[35]  Georgi M. Dimirovski,et al.  L 2-Gain analysis and control synthesis of uncertain discrete-time switched linear systems with time delay and actuator saturation , 2011, Int. J. Control.

[36]  El-Kébir Boukas,et al.  Stochastic Switching Systems: Analysis and Design , 2005 .

[37]  Hongye Su,et al.  Robust H-infinity control for uncertain discrete-time Markovian jump systems with actuator saturation , 2011 .

[38]  Luca Zaccarian,et al.  Linear discrete-time global and regional anti-windup: an LMI approach , 2009, Int. J. Control.

[39]  Jianbin Qiu,et al.  Static-Output-Feedback ${\mathscr H}_{\bm \infty }$ Control of Continuous-Time T - S Fuzzy Affine Systems Via Piecewise Lyapunov Functions , 2013, IEEE Transactions on Fuzzy Systems.

[40]  Sophie Tarbouriech,et al.  Anti-windup design with guaranteed regions of stability for discrete-time linear systems , 2004, Proceedings of the 2004 American Control Conference.

[41]  Zongli Lin,et al.  An anti-windup design for polytopic systems by a parameter-dependent Lyapunov function approach , 2005, 2005 International Conference on Control and Automation.

[42]  Peng Shi,et al.  Fault-Tolerant Control for Nonlinear Markovian Jump Systems via Proportional and Derivative Sliding Mode Observer Technique , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[43]  Bo Li,et al.  Robust exponential H∞ control for uncertain time-varying delay systems with input saturation: A Markov jump model approach , 2014, Appl. Math. Comput..

[44]  Hongjiu Yang,et al.  Analysis and design for delta operator systems with actuator saturation , 2014, Int. J. Control.

[45]  Zhongjie Wang,et al.  Stability of Markovian jump systems with generally uncertain transition rates , 2013, J. Frankl. Inst..

[46]  Jin Bae Park,et al.  Decentralized adaptive stabilization of interconnected nonlinear systems with unknown non-symmetric dead-zone inputs , 2009, Autom..

[47]  E. Boukas,et al.  H∞-Control for Markovian Jumping Linear Systems with Parametric Uncertainty , 1997 .

[48]  Alberto Bemporad,et al.  Anti-windup synthesis via sampled-data piecewise affine optimal control , 2004, Autom..

[49]  Magdi S. Mahmoud,et al.  Methodologies for Control of Jump Time-Delay Systems , 2003 .

[50]  Hamid Reza Karimi,et al.  New approach to delay-dependent H∞ control for continuous-time Markovian jump systems with time-varying delay and deficient transition descriptions , 2015, J. Frankl. Inst..

[51]  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).

[52]  E. Boukas,et al.  Robust control of uncertain discrete-time Markovian jump systems with actuator saturation , 2006 .

[53]  Alexandre Trofino,et al.  Mode-Independent ${\cal H}_{\infty}$ Filters for Markovian Jump Linear Systems , 2006, IEEE Transactions on Automatic Control.

[54]  Matthew C. Turner,et al.  Anti-windup compensation for systems with sensor saturation: a study of architecture and structure , 2009, Int. J. Control.

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

[56]  E. Boukas,et al.  H∞ control for discrete‐time Markovian jump linear systems with partly unknown transition probabilities , 2009 .