State feedback control of Markovian jump systems with Markovian delay and uncertain transition probability

This paper is addressed with the networked-based state feedback control issue for a class of discrete-time Markovian jump linear systems (MJLS) with the random sensor to controller (S-C) time delay and the uncertain transition probability. Considering the random time delay occurring in feedback communication link, the resulting closed-loop system is modeled as a discrete-time Markovian jump linear delay system governed by two mutual independence Markov chains. A new stability criterion is established within the Markovian jump framework by applying a Lyapunov stability theory and linear matrix inequalities (LMI) technique. A simulation example illustrates the validity and feasibility of the method.

[1]  James Lam,et al.  Analysis and Synthesis of Markov Jump Linear Systems With Time-Varying Delays and Partially Known Transition Probabilities , 2008, IEEE Transactions on Automatic Control.

[2]  Hamid Reza Karimi,et al.  Output-Feedback-Based $H_{\infty}$ Control for Vehicle Suspension Systems With Control Delay , 2014, IEEE Transactions on Industrial Electronics.

[3]  Mirza Hamedulla Baig,et al.  Stabilization of networked control systems with random delays , 2012 .

[4]  Jianbin Qiu,et al.  Control Synthesis for a Class of Linear Network-Based Systems With Communication Constraints , 2013, IEEE Transactions on Industrial Electronics.

[5]  Li Qiu,et al.  Output Feedback Stabilization of Networked Control Systems with Uncertain Transition Probability Matrix , 2013, ICONS.

[6]  P. Kiessler.  Stochastic Switching Systems: Analysis and Design , 2008 .

[7]  Bo Yu,et al.  Robust mixed H2/H∞ control of networked control systems with random time delays in both forward and backward communication links , 2011, Autom..

[8]  Huijun Gao,et al.  Distributed Synchronization in Networks of Agent Systems With Nonlinearities and Random Switchings , 2013, IEEE Transactions on Cybernetics.

[9]  Li Qiu,et al.  H2/H∞ control of networked control system with random time delays , 2011, Science China Information Sciences.

[10]  Dong Yue,et al.  A Delay System Method for Designing Event-Triggered Controllers of Networked Control Systems , 2013, IEEE Transactions on Automatic Control.

[11]  Fei Liu,et al.  Stabilization of Networked Control Systems With Random Delays , 2011, IEEE Transactions on Industrial Electronics.

[12]  Oswaldo Luiz do Valle Costa,et al.  Stochastic Stability of Jump Discrete-Time Linear Systems With Markov Chain in a General Borel Space , 2014, IEEE Transactions on Automatic Control.

[13]  Dong Yue,et al.  Stabilization of Systems With Probabilistic Interval Input Delays and Its Applications to Networked Control Systems , 2009, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[14]  Baocang Ding,et al.  Model predictive control of linear systems over networks with data quantizations and packet losses , 2013, Autom..

[15]  Young Soo Moon,et al.  Delay-dependent robust stabilization of uncertain state-delayed systems , 2001 .

[16]  Huijun Gao,et al.  Distributed H∞ Filtering for a Class of Markovian Jump Nonlinear Time-Delay Systems Over Lossy Sensor Networks , 2013, IEEE Transactions on Industrial Electronics.