基于观测器的马尔科夫跳变系统的滑模控制问题

Research on Markov Jump System Based on Observer

针对系统具有不可测量状态的实际情况,研究了带有不确定项和扰动输入的时变时滞Markov切换系统,设计了模态依赖的观测器和滑模控制器,构造了积分滑模面,并通过估计变量得到误差系统。通过构造合适的模态依赖的李雅普诺夫函数,运用线性矩阵不等式理论进行求解,得到了使闭环系统渐近稳定并且满足混合Η_(∞)和无源的性能指标的充分条件,并建立了观测器和控制器的增益矩阵。最后,通过仿真证明了所提理论的合理性和优越性。

In view of the potential situation that the system has unmeasurable state,the time-varying delay Markov switched system with uncertainty and disturbance input isstudied.The modal dependent observer and sliding mode controller are designed,the integral sliding mode surface is constructed,and the error system is obtained by estimating the variables.In addition,according to the construction of appropriate modal dependent Lyapunov function,it is solved by using the theory of linear matrix inequality.Thesufficient conditions are obtained for the closed-loop system to be asymptotically stable and to satisfy the mixed Η_(∞)and passive performance indexes,and the gain matrices of observer and controller are obtained.Finally,the effectiveness and superiority of the proposed method are verified by simulation examples.