一类离散Markov跳跃系统基于状态观测器的鲁棒H_∞控制

Robust observer-based H_∞ control for a class of discrete-time Markovian jump systems

研究了具有不确定性的模式依赖时滞离散Markov跳跃系统基于状态观测器的鲁棒H∞控制问题。目的是构建依赖于系统模式的观测器和控制器,使得闭环系统是随机稳定的且具有较好的H∞干扰抑制性能。通过选取合适的随机Lyapunov函数,利用线性矩阵不等式,给出了鲁棒H∞控制器存在的时滞依赖条件。基于锥补线性化算法对控制器进行求解,得到了模式依赖观测器和控制器。最后通过数值仿真证明了本文方法的可行性。

The robust H∞ observer-based control problem for a class of discrete-time Markovian jump systems with mode-dependent time delay and norm bounded uncertainties was investigated. Atlention was focused on constructing a mode-dependent observer and controller to guarantee the closed-loop system stable stochastically with a good H∞ disturbance attenuation behavior. A delay-dependent condition sufficient for the existence of H∞ controller was given by choosing a suitable type of stochastic Lyapunov function and using the linear matrix inequality. The mode-dependent observer and controller were obtained through solving the controller by the cone complementasity linearization algorithm. Numerical simulation illustrated the feasibility of the proposed technique.