Finite-time H∞ control for T-S fuzzy descriptor semi-Markov jump systems via static output feedback

Abstract This paper is concerned with the finite-time static output feedback H ∞ controller design problem for a type of nonlinear continuous-time descriptor semi-Markov jump systems (S-MJSs) via Takagi–Sugeno (T–S) fuzzy model, where the transition rates are time-varying and dependent on sojourn time. Firstly, based on the stochastic Lyapunov functional, sufficient conditions on singular stochastic H ∞ finite-time boundedness ( SS H ∞ FTB ) for continuous-time T–S fuzzy descriptor S-MJSs are given. Then, in order to design the static output feedback controller easily, the closed-loop system is represented in an augmented form. Furthermore, based on the lower and upper bounds of the time-varying transition rates, and by using the matrix inequality decoupling technique, a novel linear matrix inequality (LMI) condition on SS H ∞ FTB of closed-loop system is presented. Meanwhile, the static output feedback controller is developed in terms of LMIs. The proposed design method doesn't impose any constraints on system matrices or slack variables, which shows less conservative results. Lastly, numerical examples are given to demonstrate the effectiveness of the obtained methods.

[1]  Ju H. Park,et al.  Robust static output feedback H∞ control for uncertain fuzzy systems , 2015, Fuzzy Sets Syst..

[2]  Nikolaos Limnios,et al.  Semi-Markov Chains and Hidden Semi-Markov Models toward Applications: Their Use in Reliability and DNA Analysis , 2008 .

[3]  Yan Shi,et al.  Dissipativity Analysis for Discrete Time-Delay Fuzzy Neural Networks With Markovian Jumps , 2016, IEEE Transactions on Fuzzy Systems.

[4]  Ricardo C. L. F. Oliveira,et al.  ℋ2 and ℋ∞ filter design for polytopic continuous‐time Markov jump linear systems with uncertain transition rates , 2015 .

[5]  Guoliang Wang,et al.  Stabilization of discrete‐time singular Markovian jump repeated vector nonlinear systems , 2016 .

[6]  Jimin Wang,et al.  Finite-time stabilization for nonlinear discrete-time singular Markov jump systems with piecewise-constant transition probabilities subject to average dwell time , 2017, J. Frankl. Inst..

[7]  Peng Shi,et al.  Stochastic stability of Ito differential equations with semi-Markovian jump parameters , 2006, IEEE Transactions on Automatic Control.

[8]  John Leth,et al.  Stochastic stability of systems with semi-Markovian switching , 2014, Autom..

[9]  Mohamed Darouach,et al.  Further Enhancement on Robust $H_{\infty}$ Control Design for Discrete-Time Singular Systems , 2014, IEEE Transactions on Automatic Control.

[10]  Shen Yan,et al.  Finite-time H∞ static output control of Markov jump systems with an auxiliary approach , 2016, Appl. Math. Comput..

[11]  El Kebir Boukas,et al.  Static output feedback control for stochastic hybrid systems: LMI approach , 2006, Autom..

[12]  Fei Liu,et al.  Finite-Time $H_{\infty}$ Fuzzy Control of Nonlinear Jump Systems With Time Delays Via Dynamic Observer-Based State Feedback , 2012, IEEE Transactions on Fuzzy Systems.

[13]  Zheng-Guang Wu,et al.  Output feedback stabilization for discrete singular systems with random abrupt changes , 2010 .

[14]  P.-C. G. Vassiliou,et al.  Fuzzy semi-Markov migration process in credit risk , 2013, Fuzzy Sets Syst..

[15]  Jimin Wang,et al.  Stability analysis and stabilization for nonlinear continuous-time descriptor semi-Markov jump systems , 2016, Appl. Math. Comput..

[16]  Shengyuan Xu,et al.  Robust Control and Filtering of Singular Systems , 2006 .

[17]  Li Li,et al.  Fuzzy Control for Nonlinear Singular Markovian Jump Systems with Time Delay , 2015 .

[18]  Qingling Zhang,et al.  H∞ fuzzy control for nonlinear time-delay singular Markovian jump systems with partly unknown transition rates , 2014, Fuzzy Sets Syst..

[19]  Yang Shi,et al.  Stochastic stability and robust stabilization of semi‐Markov jump linear systems , 2013 .

[20]  J. Geromel,et al.  Discrete‐time H∞ output feedback for Markov jump systems with uncertain transition probabilities , 2013 .

[21]  Jianbin Qiu,et al.  Robust and non-fragile static output feedback control for continuous-time semi-Markovian jump systems , 2016 .

[22]  Hak-Keung Lam,et al.  Design of a Polynomial Fuzzy Observer Controller With Sampled-Output Measurements for Nonlinear Systems Considering Unmeasurable Premise Variables , 2015, IEEE Transactions on Fuzzy Systems.

[23]  E. Boukas,et al.  New approach to H ∞ control for Markovian jump singular systems , 2010 .

[24]  James Lam,et al.  Static output-feedback stabilization of discrete-time Markovian jump linear systems: A system augmentation approach , 2010, Autom..

[25]  Chenghui Zhang,et al.  Stability and robust stabilisation for a class of non-linear uncertain discrete-time descriptor Markov jump systems , 2012 .

[26]  Qingling Zhang,et al.  Non-fragile static output feedback control for singular T-S fuzzy delay-dependent systems subject to Markovian jump and actuator saturation , 2016, J. Frankl. Inst..

[27]  Xiaowu Mu,et al.  Robust finite-time H∞ control of singular stochastic systems via static output feedback , 2012, Appl. Math. Comput..

[28]  Lixian Zhang,et al.  H∞ estimation for discrete-time piecewise homogeneous Markov jump linear systems , 2009, Autom..

[29]  Ricardo C. L. F. Oliveira,et al.  ℋ∞ and ℋ2 control design for polytopic continuous-time Markov jump linear systems with uncertain transition rates , 2015 .

[30]  Huaguang Zhang,et al.  Dissipativity Analysis and Synthesis for a Class of T–S Fuzzy Descriptor Systems , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[31]  Ju H. Park,et al.  Reliable mixed H∞/passive control for T-S fuzzy delayed systems based on a semi-Markov jump model approach , 2017, Fuzzy Sets Syst..

[32]  Yuanqing Xia,et al.  Control for discrete singular hybrid systems , 2008, Autom..

[33]  Chun-Hsiung Fang,et al.  Robust H∞ fuzzy static output feedback control of T-S fuzzy systems with parametric uncertainties , 2007, Fuzzy Sets Syst..

[34]  Dan Ye,et al.  Robust H ∞ static output control of discrete Markov jump linear systems with norm bounded uncertainties , 2014 .

[35]  Jianbin Qiu,et al.  Sliding mode control for semi-Markovian jump systems via output feedback , 2017, Autom..

[36]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[37]  Ligang Wu,et al.  Output Feedback Control of Markovian Jump Repeated Scalar Nonlinear Systems , 2014, IEEE Transactions on Automatic Control.

[38]  Salim Labiod,et al.  Robust H∞ static output feedback stabilization of T-S fuzzy systems subject to actuator saturation , 2012 .

[39]  L. Dai,et al.  Singular Control Systems , 1989, Lecture Notes in Control and Information Sciences.

[40]  Patrizio Colaneri,et al.  Stability and Stabilization of Discrete-Time Semi-Markov Jump Linear Systems via Semi-Markov Kernel Approach , 2016, IEEE Transactions on Automatic Control.

[41]  Pierre Apkarian,et al.  Parameterized linear matrix inequality techniques in fuzzy control system design , 2001, IEEE Trans. Fuzzy Syst..