马尔科夫切换型时滞系统的稳定性

Stability of Markov Switching Delay Systems

马尔科夫切换型时滞系统是能很好地描述具有随机性同时又具有时滞的一类系统,而稳定性是其研究的基础。通过选取合适的Lyapunov-Krasovskii泛函,利用线性矩阵不等式和Schur补引理得到了依赖于时滞的稳定性判据,理论上说明了所考虑系统在足够小的时滞条件下可以达到渐近稳定。最后通过Matlab LMIs Toolbox可以找到可行的矩阵解,并且借助Matlab LMIs Toolbox进行了数值仿真,说明了所得结论的有效性。

Markov switching delay system is a kind of systems which can be well described as thesystem with random and time delay. The stability is the foundation of its research. By choosing aappropriate Lyapunov-Krasovskii functional, using linear matrix inequality and Schur lemma, thestability criteria dependent on the sufficient small delay for the considered system can achieveasymptotic stability. Finally, the feasible matrix solution can be found by LMIs Toolbox Matlab, andthe numerical simulation was designed by means of LMIs Toolbox Matlab, which shows theeffectiveness of the conclusion.