Finite-Time Passivity and Passification for Stochastic Time-Delayed Markovian Switching Systems with Partly Known Transition Rates

Finite-time passivity and passification is assessed for stochastic time-delayed Markovian switching systems with partly known transition rates. By employing an appropriate mode-dependent Lyapunov function and some appropriate free-weighting matrices, a state feedback controller is constructed such that the resulting closed-loop system is finite-time bounded and satisfies the given passive constraint condition. Expressed as linear matrix inequalities, some sufficient conditions for solvability of the problem are derived. Finally, an example is given to demonstrate the validity of the main results.

[1]  Francesco Amato,et al.  Finite-time control of discrete-time linear systems: Analysis and design conditions , 2010, Autom..

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

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

[4]  Fei Liu,et al.  Disturbance Rejection for Markov Jump Systems with Partly Unknown Transition Probabilities and Saturation , 2013, Circuits Syst. Signal Process..

[5]  Ligang Wu,et al.  Sliding mode control with bounded L2 gain performance of Markovian jump singular time-delay systems , 2012, Autom..

[6]  Ashish Tiwari,et al.  Symbolic Systems Biology: Hybrid Modeling and Analysis of Biological Networks , 2004, HSCC.

[7]  Renquan Lu,et al.  H∞ filtering for singular systems with communication delays , 2010, Signal Process..

[8]  Qi Huang,et al.  Exponential L2-L∞ filtering for a class of stochastic system with Markovian jump parameters and mixed mode-dependent time-delays , 2014 .

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

[10]  Fei Liu,et al.  Optimal finite-time passive controller design for uncertain nonlinear Markovian jumping systems , 2014, J. Frankl. Inst..

[11]  Zheng-Guang Wu,et al.  Delay-dependent passivity for singular Markov jump systems with time-delays , 2013, Commun. Nonlinear Sci. Numer. Simul..

[12]  Ju H. Park,et al.  Stochastic stability analysis for discrete-time singular Markov jump systems with time-varying delay and piecewise-constant transition probabilities , 2012, J. Frankl. Inst..

[13]  X. Mao.  Stability of stochastic differential equations with Markovian switching , 1999 .

[14]  Xian Zhang,et al.  Robust passive filtering for neutral-type neural networks with time-varying discrete and unbounded distributed delays , 2013, J. Frankl. Inst..

[15]  Yonggui Kao,et al.  Robust Guaranteed Cost Observer Design for Singular Markovian Jump Time-Delay Systems with Generally Incomplete Transition Probability , 2014 .

[16]  Ligang Wu,et al.  An Improved Integral Inequality to Stability Analysis of Genetic Regulatory Networks With Interval Time-Varying Delays , 2015, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[17]  S. Shankar Sastry,et al.  Conflict resolution for air traffic management: a study in multiagent hybrid systems , 1998, IEEE Trans. Autom. Control..

[18]  Huijun Gao,et al.  Fault-tolerant control of Markovian jump stochastic systems via the augmented sliding mode observer approach , 2014, Autom..

[19]  Yongduan Song,et al.  Finite-time H∞ filtering for discrete-time Markovian jump systems , 2013, J. Frankl. Inst..

[20]  Xian Zhang,et al.  Robust stability of stochastic genetic regulatory networks with time-varying delays: a delay fractioning approach , 2012, Neural Computing and Applications.

[21]  Bo Song,et al.  Mixed H∞ and passive filtering for singular systems with time delays , 2013, Signal Process..

[22]  Vladimir L. Kharitonov,et al.  Stability of Time-Delay Systems , 2003, Control Engineering.

[23]  Xian Zhang,et al.  Delay-dependent robust H∞ filtering of uncertain stochastic genetic regulatory networks with mixed time-varying delays , 2015, Neurocomputing.

[24]  Yuzhen Wang,et al.  Finite-time stability analysis and H∞ control for a class of nonlinear time-delay Hamiltonian systems , 2013, Autom..

[25]  Junwei Lu,et al.  Robust H∞ filter design for uncertain stochastic Markovian jump Hopfield neural networks with mode-dependent time-varying delays , 2014, Neurocomputing.

[26]  Guoliang Chen,et al.  Improved passivity analysis for neural networks with Markovian jumping parameters and interval time-varying delays , 2015, Neurocomputing.

[27]  W. Zheng,et al.  Exponential H ∞  filtering for stochastic Markovian jump systems with time delays , 2014 .

[28]  Shengyuan Xu,et al.  Passivity-based Control for Markovian Jump Systems via Retarded Output Feedback , 2012, Circuits Syst. Signal Process..

[29]  Xian Zhang,et al.  Robust H∞ Control for a Class of Uncertain Neutral Stochastic Systems with Mixed Delays: a CCL Approach , 2013, Circuits Syst. Signal Process..

[30]  Zhiqiang Zuo,et al.  Finite-time stochastic stability and stabilisation of linear discrete-time Markovian jump systems with partly unknown transition probabilities , 2012 .

[31]  Ligang Wu,et al.  Observer-based adaptive sliding mode control for nonlinear Markovian jump systems , 2016, Autom..

[32]  Fei Liu,et al.  On Delay-Dependent Stability of Markov Jump Systems with Distributed Time-Delays , 2011, Circuits Syst. Signal Process..

[33]  Shuping He,et al.  Non-fragile passive controller design for nonlinear Markovian jumping systems via observer-based controls , 2015, Neurocomputing.

[34]  Z. Zeng,et al.  Passivity and passification of stochastic impulsive memristor‐based piecewise linear system with mixed delays , 2015 .

[35]  Xian Zhang,et al.  Guaranteed cost control for uncertain genetic regulatory networks with interval time-varying delays , 2014, Neurocomputing.

[36]  Yun Chen,et al.  Delay-Dependent Robust Control for Uncertain Stochastic Time-Delay Systems , 2008 .

[37]  João Pedro Hespanha,et al.  Stochastic Hybrid Systems: Application to Communication Networks , 2004, HSCC.

[38]  Hui Li,et al.  Quantized H∞ Filtering for Singular Time-varying Delay Systems with Unreliable Communication Channel , 2012, Circuits Syst. Signal Process..

[39]  Wenhai Qi,et al.  State feedback controller design for singular positive Markovian jump systems with partly known transition rates , 2015, Appl. Math. Lett..

[40]  Ju H. Park,et al.  Finite-time synchronization control for uncertain Markov jump neural networks with input constraints , 2014, Nonlinear Dynamics.

[41]  Yueying Wang,et al.  Delay-Dependent Passivity and Passification for Uncertain Singularly Perturbed Markovian Jump Systems with Time-Varying Delay , 2012, Circuits Syst. Signal Process..

[42]  Tao Li,et al.  Adaptive Fault-Tolerant Stochastic Shape Control With Application to Particle Distribution Control , 2015, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[43]  Wenhai Qi,et al.  Finite-time H∞ control for stochastic time-delayed Markovian switching systems with partly known transition rates and nonlinearity , 2016, Int. J. Syst. Sci..

[44]  Carlo Cattani,et al.  Application of Local Fractional Series Expansion Method to Solve Klein-Gordon Equations on Cantor Sets , 2014 .

[45]  Feng Liu,et al.  Passivity-based control of hybrid impulsive and switching systems with singular structure , 2013, J. Frankl. Inst..

[46]  Caixia Liu,et al.  Observer-based finite-timeH∞control of discrete-time Markovian jump systems , 2013, Applied Mathematical Modelling.

[47]  Yue Wang,et al.  On Passivity of a Class of Discrete-Time Switched Nonlinear Systems , 2014, IEEE Transactions on Automatic Control.