基于观测器的不确定时滞Markov跳变系统H_∞控制

Observer-based H_∞ control for uncertain time-delay systems with Markov jumps

讨论了一类线性不确定时滞Markov跳变系统的控制问题,针对能量有界的输入噪声,设计了基于观测器的优化鲁棒H∞控制器。基于鲁棒控制理论,通过对重构的观测器系统的分析,提出了使得系统随机稳定且满足一定输入输出H∞增益的模态依赖的控制器存在条件。结合构造的Lyapunov函数和线性矩阵不等式变换,给出了H∞控制器的设计方法,并将其描述为一个优化问题。基于观测器设计的优化H∞控制器使系统具有随机稳定性,状态的跟踪性能好,抑制干扰能力强,满足所给的范数指标。仿真示例说明了设计方法的有效性。

The control problem of a class of uncertain tlme-delay linear systems with Markov jumps is studied. An observer-based optimized robust H∞ controller is designed for a given system with energy bounded noise inputs. Based on the robust control theory, the sufficient condition for the existence of mode-dependent H∞ controller is given by analyzing the reconstructed observer system. By constructing proper Lyapunov function and applying linear matrix inequality, the design method of the controller is derived and described as an optimization one. The presented observer-based optimized robust H∞ controller makes the systems stochastically stable, has better abilities of state tracking and disturbances restraining, and satisfies the presented norm index. Simulation results demonstrate the validity of the proposed approach.