New result on delay-dependent stability for Markovian jump time-delay systems with partial information on transition probabilities

This paper focuses on the delay-dependent stability for a kind of Markovian jump time-delay systems ( MJTDSs ), whose transition rates are incompletely known. In order to reduce the computational complexity and achieve better performance, auxiliary function-based double integral inequality is combined with extended Wirtingerʼ s inequality and Jensen inequality to deal with the double integral and the triple integral in augmented Lyapunov-Krasovskii function ( ALKF ) and their weak infinitesimal generator respectively, the more accurate approximation bounds with a fewer variables are derived. As a result, less conservative stability criteria are proposed in this paper. Finally, numerical examples are given to show the effectiveness and the merits of the proposed method.

[1]  PooGyeon Park,et al.  Reciprocally convex approach to stability of systems with time-varying delays , 2011, Autom..

[2]  Zhichen Li,et al.  Improved stability and stabilization design for networked control systems using new quadruple-integral functionals. , 2016, ISA transactions.

[3]  Frédéric Gouaisbaut,et al.  Complete Quadratic Lyapunov functionals using Bessel-Legendre inequality , 2014, 2014 European Control Conference (ECC).

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

[5]  Frédéric Gouaisbaut,et al.  Wirtinger-based integral inequality: Application to time-delay systems , 2013, Autom..

[6]  H. Kushner.  Stochastic Stability and Control , 2012 .

[7]  X. Mao,et al.  Stochastic Differential Equations and Applications , 1998 .

[8]  R. Rakkiyappan,et al.  Exponential synchronization of Markovian jumping neural networks with partly unknown transition probabilities via stochastic sampled-data control , 2014, Neurocomputing.

[9]  Amir Averbuch,et al.  Interacting Multiple Model Methods in Target Tracking: A Survey , 1988 .

[10]  Shouming Zhong,et al.  Finite-time H∞ control for a class of discrete-time Markovian jump systems with partly unknown time-varying transition probabilities subject to average dwell time switching , 2015, Int. J. Syst. Sci..

[11]  Qing-Guo Wang,et al.  Delay-range-dependent stability for systems with time-varying delay , 2007, Autom..

[12]  Qing-Long Han,et al.  Event-based H∞ filtering for sampled-data systems , 2015, Autom..

[13]  James Lam,et al.  Stability and Stabilization for Markovian Jump Time-Delay Systems With Partially Unknown Transition Rates , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[14]  Gang Chen,et al.  Stability analysis of systems with timevarying delay via a novel Lyapunov functional , 2019, IEEE/CAA Journal of Automatica Sinica.

[15]  Min Wu,et al.  H∞ control for discrete‐time Markovian jump systems with partial information on transition probabilities , 2013 .

[16]  Huaguang Zhang,et al.  Stochastic synchronization for Markovian coupled neural networks with partial information on transition probabilities , 2015, Neurocomputing.

[17]  E. Boukas,et al.  Stability and Stabilization of Markovian Jump Linear Systems with Partly Unknown Transition Probabilities , 2008 .

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

[19]  Yong He,et al.  Stability analysis of systems with time-varying delay via relaxed integral inequalities , 2016, Syst. Control. Lett..

[20]  PooGyeon Park,et al.  Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems , 2015, J. Frankl. Inst..

[21]  Diana Baader,et al.  Stability Analysis And Robust Control Of Time Delay Systems , 2016 .

[22]  Jian Sun,et al.  Improved stability criteria for linear systems with time-varying delay , 2010 .

[23]  ParkPooGyeon,et al.  Reciprocally convex approach to stability of systems with time-varying delays , 2011 .

[24]  Yong He,et al.  Stability Analysis for Delayed Neural Networks Considering Both Conservativeness and Complexity , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[25]  Yong He,et al.  State estimation for Markovian jump systems with time-varying delay and partial information on transition probabilities [Brief Paper] , 2012 .

[26]  Guang-Hong Yang,et al.  H 2 state feedback controller design for continuous Markov jump linear systems with partly known information , 2012, Int. J. Syst. Sci..