执行器饱和的随机Markov跳变系统非脆弱有限时间镇定

研究了带有执行器饱和与转移概率部分已知的随机Markov跳变系统的非脆弱有限时间镇定问题.转移概率部分已知包含转移概率完全已知和转移概率完全未知两类特殊的情况.首先基于参数依赖型Lyapunov函数和自由权矩阵方法,对随机Markov饱和跳变系统的镇定进行了研究,提出了有限时间稳定的充分条件.然后利用线性矩阵不等式的方法实现了非脆弱有限时间状态反馈控制器与吸引域最大估计值的求解.最后通过四模态随机Markov跳变系统的数值例子验证了结论的有效性.

Non-fragile Finite-Time Stabilization for Stochastic Markov Jump Systems with Actuator Saturation

This paper dealed with the problem of finite-time stabilization for a class of stochastic Markov jump systems with both actuator saturation and partly known transition probabilities. Partly known transition probabilities covered completely known transition probabilities and completely unknown transition probabilities as two special cases. Firstly， by use of parameter-dependent Lyapunov function and free-connection weighting matrices， the problem of finite-time stabilization of stochastic Markov jump systems with actuator saturation was analyzed and sufficient conditions for finite-time stability were proposed. The procedure of solution for the non-fragile finite-time state feedback controller and the maximum domain of attraction were built in the form of linear matrix inequalities (LMIs). Finally， a numerical example about four modes with Markov jump parameters was given to show the validity of the results.