The problem of delay-dependent stability in the mean square sense for stochastic systems with time-varying delays, Markovian switching and nonlinearities is investigated. Both the slowly time-varying delays and fast time-varying delays are considered. Based on a linear matrix inequality approach, delay-dependent stability criteria are derived by introducing some relaxation matrices which can be chosen properly to lead to a less conservative result. Numerical examples are given to illustrate the effectiveness of the method and significant improvement of the estimate of stability limit over some existing results in the literature.

Delay-dependent exponential stability of stochastic systems with time-varying delay, nonlinearity, and Markovian switching

Brief paper: H∞ filtering for 2D Markovian jump systems

SUMMARY

The semi-Markov jump linear system (S-MJLS) is more general than the Markov jump linear system (MJLS) in modeling some practical systems. Unlike the constant transition rates in the MJLS, the transition rates of the S-MJLS are time varying. This paper focuses on the robust stochastic stability condition and the robust control design problem for the S-MJLS with norm-bounded uncertainties. The infinitesimal generator for the constructed Lyapunov function is first derived. Numerically solvable sufficient conditions for the stochastic stability of S-MJLSs are then established in terms of linear matrix inequalities. To reduce the conservativeness of the stability conditions, we propose to incorporate the upper and lower bounds of the transition rate and meanwhile apply a new partition scheme. The robust state feedback controller is accordingly developed. Simulation studies and comparisons demonstrate the effectiveness and advantages of the proposed methods. Copyright © 2012 John Wiley & Sons, Ltd.

Stochastic stability and robust stabilization of semi-Markov jump linear systems

This paper proposes a new approach, namely, the delay partitioning approach, to solving the problems of stability analysis and stabilization for continuous time-delay Takagi-Sugeno fuzzy systems. Based on the idea of delay fractioning, a new method is proposed for the delay-dependent stability analysis of fuzzy time-delay systems. Due to the instrumental idea of delay partitioning, the proposed stability condition is much less conservative than most of the existing results. The conservatism reduction becomes more obvious with the partitioning getting thinner. Based on this, the problem of stabilization via the so-called parallel distributed compensation scheme is also solved. Both the stability and stabilization results are further extended to time-delay fuzzy systems with time-varying parameter uncertainties. All the results are formulated in the form of linear matrix inequalities (LMIs), which can be readily solved via standard numerical software. The advantage of the results proposed in this paper lies in their reduced conservatism, as shown via detailed illustrative examples. The idea of delay partitioning is well demonstrated to be efficient for conservatism reduction and could be extended to solving other problems related to fuzzy delay systems.

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Stability and Stabilization of Delayed T--S Fuzzy Systems: A Delay Partitioning Approach

Stability analysis for stochastic hybrid systems

This paper is concerned with the delay-dependent stability for a class of stochastic
uncertain systems with time delay and Markovian jump parameters. The uncertainties
considered in this paper are norm-bounded and governed by the Markov process. Un like
the topics in the existing literature, the stability criterion is expressed in terms of linear
matrix inequalities, which can be efficiently solved by using a convex-optimization algorithm.
Finally, a numerical example is given to illustrate the effectiveness of the proposed
method.

Jian an Fang

Papers

Delay-Dependent Robust Stability of Stochastic Uncertain Systems with Time Delay and Markovian Jump Parameters