Stability Analysis for Markovian Jump Neutral Systems with Mixed Delays and Partially Known Transition Rates

Lianglin Xiong,Jing Lei,Xiaobing Zhou,Jie Qiu

doi:10.1155/2012/450168

Lianglin Xiong, Jing Lei + Show 2 more

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https://doi.org/10.1155/2012/450168

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Abstract

The delay-dependent stability problem is studied for Markovian jump neutral systems with partial information on transition probabilities, and the considered delays are mixed and model dependent. By constructing the new stochastic Lyapunov-Krasovskii functional, which combined the introduced free matrices with the analysis technique of matrix inequalities, a sufficient condition for the systems with fully known transition rates is firstly established. Then, making full use of the transition rate matrix, the results are obtained for the other case, and the uncertain neutral Markovian jump system with incomplete transition rates is also considered. Finally, to show the validity of the obtained results, three numerical examples are provided.

Highlights

A switched system is a dynamic system consisted of a number of subsystems and a rule that manages the switching between these subsystems
It should be mentioned that Theorem 4.1 is an extension of 2.1 to uncertain neutral markovian jump systems 4.1 with incomplete transition descriptions
The main contribution of this paper contains the following two-fold: one is the extension of delay-dependent stability conditions for markovian jump delay systems to markovian neutral jump systems; the other is the new method presented to decrease the conservative brought by the markovian jump with partly known transition probabilities

Summary

Introduction

A switched system is a dynamic system consisted of a number of subsystems and a rule that manages the switching between these subsystems. 33 provided with a new approach to obtain the necessary and sufficient conditions for markovian jump linear systems with incomplete transition probabilities, which may be appropriate to discuss the counterpart of delay systems Most of these improved results just require some free matrices or the knowledge of the known elements in transition rate matrix, such as the bounds or structures of uncertainties, and some else of the unknown elements need not be considered. The number of matrix inequalities conditions obtained in this paper is much more than some existing results due to the introduced free matrices based on the system itself and the information of transition probabilities in this paper, which may increase the complexity of computation It would decrease the conservativeness for the delay-dependent stability conditions. Two numerical examples are provided to illustrate the effectiveness of our results

Problem Statement and Preliminaries

Stability Analysis for Neutral Markovian Jump Systems

Extension to Uncertain Neutral Markov Jump Systems

Examples

Conclusion