Stabilization for Piecewise Homogeneous Markov Jump Systems Subject to Actuator Saturation

doi:10.12068/j.issn.1005-3026.2017.04.002

Abstract

Abstract: The stabilization problem was studied for a class of Markov jump linear systems subject to actuator saturation， whose transition rates are piecewise homogeneous. Firstly， by using appropriate Lyapunov functional and ellipsoidal invariant set theory， the attraction domain of system in mean square sense was estimated to get the sufficient conditions with constraints of linear matrix inequalities for the closed-loop systems. Then， a convex optimization problem was solved to get the maximum domain of attraction in mean square sense and the state feedback controller gain. Finally， the effectiveness of the results was verified by a numerical example.

Key words: actuator saturation, Markov jump systems, piecewise homogeneous, linear matrix inequalities, convex optimization

CLC Number:

TP273

QI Wen-hai， LI Xin， GAO Xian-wen. Stabilization for Piecewise Homogeneous Markov Jump Systems Subject to Actuator Saturation[J]. Journal of Northeastern University Natural Science, 2017, 38(4): 462-466.

References

[1]Dong J W，Kim W J.Markov-chain-based output feedback control for stabilization of networked control systems with random time delays and packet losses［J］.International Journal of Control，Automation and Systems，2012，10(5):1013-1022.
[2]Shen L J，Buscher U.Solving the serial batching problem in job shop manufacturing systems［J］.European Journal of Operational Research，2012，221(1):14-26.
[3]Yin Y，Shi P，Liu F，et al.Gain-scheduled fault detection on stochastic nonlinear systems with partially known transition jump rates［J］.Nonlinear Analysis:Real World Applications，2012，13:359-369.
[4]Mao X R，Yuan C G.Stochastic differential equations with Markovian switching［M］.London:Imperial College Press，2006.
[5]Zhang L X.H_∞ estimation for discrete-time piecewise homogeneous Markov jump linear systems［J］.Automation，2009，45(11):2570-2576.
[6]Mao X R.Stability of stochastic differential equations with Markovian switching［J］.Stochastic Process and Their Applications，1999，79(1):45-67.
[7]Boukas E K.Stochastic switching systems:analysis and design［M］.Berlin:Birkhauser，2005.
[8]Zhang L，Boukas E K.Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities［J］.Automatica，2009，45(2):463-468.
[9]Zhang Y，He Y，Wu M，et al.Stabilization for Markovian jump systems with partial information on transition probability based on free-connection weighting matrices［J］.Automatica，2011，47(1):79-84.
[10]Ding Y C，Liu H.Filtering-based fault detection for a class of piecewise homogeneous Markov jump systems［J］.Mechatronics and Control，2014:759-764.
[11]Zhang L.H-infinity control of a class of piecewise homogeneous Markov jump linear systems［C］// Proceedings of the 7th Asian Control Conference.Hong Kong，2009:197-202.
[12]Wu Z G，Ju H P，Su H，et al.Stochastic stability analysis of piecewise homogeneous Markovian jump neural networks with mixed time-delays［J］.Journal of the Franklin Institute，2012，349(6):2136-2150.
[13]Tarbouriech S，Garcia G.Stability and stabilization of linear systems with saturating actuators［M］.London:Springer-Verlag，2011.
[14]Khalil H K.Nonlinear systems［M］.London:Macmillan，1992.
[15]Grimm G，Hatfield J，Postlethwaite I，et al.Anti-windup for stable linear systems with input saturation:an LMI based synthesis［J］.IEEE Transactions on Automatic Control，2003，48(9):1509-1525.
[16]Wu F，Grigoriadis K M，Packard A.Anti-windup controller design using linear parameter-varying control methods［J］.International Journal of Control，2000，73(12):1104-1114.
[17]Zhao J J，Wang J，Park J H，et al.Memory feedback controller design for stochastic Markov jump distributed delay systems with input saturation and partially known transition rates［J］.Nonlinear Analysis:Hybrid Systems，2015，15:52-62.
[18]Boukas E K.Stochastic output feedback of uncertain time-delay systems with saturating actuators［J］.Journal of Optimization Theory and Applications，2003，118(2):255-273.
[19]Liu H P，Boukas E K，Sun F C，et al.Controller design for Markov jumping systems subject to actuator saturation［J］.Automatica，2006，42(3):459-465.
[20]Li J N，Pan Y J，Su H Y，et al.Stochastic reliable control of a class of networked control systems with actuator faults and input saturation［J］.International Journal of Control，Automation and Systems，2014，12(3):564-571.
[21]Wang Y J，Zuo Z Q，Cui Y L.Stochastic stabilization of Markovian jump systems in the presence of partial unknown transition probabilities and actuator saturation［C］// Proceedings of 29th Chinese Control Conference.Beijing，2010:29-31.