Reliable H∞ control on saturated linear Markov jump system with uncertain transition rates and asynchronous jumped actuator failure

Abstract This paper is concerned with reliable H∞ control for saturated linear Markov jump systems with uncertain transition rates and asynchronous jumped actuator failure. The actuator failures are assumed to occur randomly under the Markov process with a different jumping mode from the system jumping mode. In considering the mixed-mode-dependent state feedback controller, both H∞ stochastic stability analysis for closed-loop system with completely accessible transition rates and uncertain transition rates are investigated. Moreover, based on the obtained stability conditions, the H∞ control problems are investigated, and the controller gains can be obtained by solving a convex optimization problem with minimizing H∞ performance as objective and linear matrix inequalities (LMIs) as constraints. The problem of designing state feedback controllers such that the estimate of the domain of attraction is enlarged is also formulated and solved as an optimization problem with LMI constraints. Simulation results are presented to illustrate the effectiveness of the proposed results.

[1]  Hui Liu,et al.  Stability analysis of continuous-time Markovian jump time-delay systems with time-varying transition rates , 2016, J. Frankl. Inst..

[2]  Dan Ye,et al.  Extended H∞ filtering of Markov jump nonlinear systems with general uncertain transition probabilities , 2015, J. Frankl. Inst..

[3]  H. Karimi,et al.  Quantized ℋ∞ Filtering for Continuous‐Time Markovian Jump Systems with Deficient Mode Information , 2015 .

[4]  Yan-Ming Fu,et al.  Parametric method for spacecraft trajectory tracking control problem with stochastic thruster fault , 2016 .

[5]  Engang Tian,et al.  Reliable control for interval time-varying delay systems subjected to actuator saturation and stochastic failure , 2012 .

[6]  Qi Huang,et al.  Decentralized finite-time H∞ filtering for interconnected Markovian jump system with interval mode-dependent delays , 2015, Appl. Math. Comput..

[7]  Fei Liu,et al.  Finite-Time Stabilization of Switching Markov Jump Systems with Uncertain Transition Rates , 2015, Circuits Syst. Signal Process..

[8]  Jianbin Qiu,et al.  Approaches to T–S Fuzzy-Affine-Model-Based Reliable Output Feedback Control for Nonlinear Itô Stochastic Systems , 2017, IEEE Transactions on Fuzzy Systems.

[9]  Yonggui Kao,et al.  Stabilization for Positive Markovian Jump Systems with Actuator Saturation , 2017, Circuits Syst. Signal Process..

[10]  Le Liu,et al.  Decentralized prescribed performance adaptive tracking control for Markovian jump uncertain nonlinear systems with input saturation , 2017 .

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

[12]  Jian Chen,et al.  Output feedback control for singular Markovian jump systems with uncertain transition rates , 2016 .

[13]  Tingshu Hu,et al.  An analysis and design method for linear systems subject to actuator saturation and disturbance , 2002, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

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

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

[16]  Zongli Lin,et al.  Output Feedback Stabilization of Linear Systems With Actuator Saturation , 2007, IEEE Transactions on Automatic Control.

[17]  Lei Guo,et al.  Decentralized output-feedback adaptive control for a class of interconnected nonlinear systems with unknown actuator failures , 2016, Autom..

[18]  Dong Yue,et al.  Decentralized adaptive neural output feedback control of a class of large-scale time-delay systems with input saturation , 2015, J. Frankl. Inst..

[19]  Friedemann Leibfritz,et al.  An LMI-Based Algorithm for Designing Suboptimal Static H2/Hinfinity Output Feedback Controllers , 2000, SIAM J. Control. Optim..

[20]  Guang-Hong Yang,et al.  Decentralized fault detection and isolation of Markovian jump interconnected systems with unknown interconnections , 2017 .

[21]  Yafeng Guo.  A Convex Method of Robust Controller Design for Markovian Jump Systems with Uncertain Transition Rates , 2014 .

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

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

[24]  Hamid Reza Karimi,et al.  Reliable Output Feedback Control of Discrete-Time Fuzzy Affine Systems With Actuator Faults , 2017, IEEE Transactions on Circuits and Systems I: Regular Papers.

[25]  José Claudio Geromel,et al.  Continuous-time state-feedback H2-control of Markovian jump linear systems via convex analysis , 1999, Autom..

[26]  Yafeng Guo.  Improved synthesis method for Markov jump systems with uncertain transition rates , 2015, J. Frankl. Inst..

[27]  James Lam,et al.  Robust H∞ control of uncertain Markovian jump systems with time-delay , 2000, IEEE Trans. Autom. Control..

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

[29]  Li Li,et al.  Decentralized robust control of uncertain Markov jump parameter systems via output feedback , 2006, 2006 American Control Conference.

[30]  Jun Cheng,et al.  New results on H∞ filtering for Markov jump systems with uncertain transition rates. , 2017, ISA transactions.

[31]  Xiao-Zheng Jin,et al.  Finite-time robust fault-tolerant control against actuator faults and saturations , 2017 .

[32]  Weihai Zhang,et al.  Stabilization of interconnected nonlinear stochastic Markovian jump systems via dissipativity approach , 2011, Autom..

[33]  Guang-Hong Yang,et al.  Robust H2 control of continuous-time Markov jump linear systems , 2008, Autom..

[34]  Guang-Hong Yang,et al.  Stabilisation of Markov jump systems with input quantisation and general uncertain transition rates , 2017 .

[35]  James Lam,et al.  Robust H 2 control of Markovian jump systems with uncertain switching probabilities , 2009, Int. J. Syst. Sci..

[36]  E. Boukas,et al.  On stabilization of uncertain linear systems with jump parameters , 1999 .

[37]  Ju H. Park,et al.  Stochastic stability analysis of piecewise homogeneous Markovian jump neural networks with mixed time-delays , 2012, J. Frankl. Inst..

[38]  Zhou Gu,et al.  Stochastic faulty actuator‐based reliable control for a class of interval time‐varying delay systems with Markovian jumping parameters , 2011 .

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

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

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

[42]  Shan Ma,et al.  Robust decentralized stabilization of Markovian jump large-scale systems: A neighboring mode dependent control approach , 2013, Autom..

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

[44]  Magdi S. Mahmoud,et al.  Decentralized Reliable Control of Interconnected Systems with Time-Varying Delays , 2009 .

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

[46]  Zhiqiang Zheng,et al.  Robust fault-tolerant control against time-varying actuator faults and saturation , 2012 .

[47]  Yijing Wang,et al.  Stochastic Stabilization of Markovian Jump Systems with Partial Unknown Transition Probabilities and Actuator Saturation , 2012, Circuits Syst. Signal Process..

[48]  Hamid Reza Karimi,et al.  Model approximation for two-dimensional Markovian jump systems with state-delays and imperfect mode information , 2015, Multidimens. Syst. Signal Process..

[49]  Hamid Reza Karimi,et al.  model reduction for continuous-time Markovian jump systems with incomplete statistics of mode information , 2014, Int. J. Syst. Sci..

[50]  Jin Bae Park,et al.  Decentralized Fuzzy Observer-Based Output-Feedback Control for Nonlinear Large-Scale Systems: An LMI Approach , 2014, IEEE Transactions on Fuzzy Systems.

[51]  Keum-Shik Hong,et al.  Delay‐range‐dependent control of nonlinear time‐delay systems under input saturation , 2016 .

[52]  Peng Shi,et al.  A survey on Markovian jump systems: Modeling and design , 2015 .