线性不确定系统经动态输出反馈的分层次控制策略

Layered control strategy of robust stabilization for uncertain systems via dynamic output feedback

利用李雅谱诺夫稳定理论及线性矩阵不等式(LMI)方法,研究了具有非结构摄动的不确定连续系统经动态输出反馈的二次鲁棒能稳定问题。推导出这类控制器存在的充分条件,即一个拟线性矩阵不等式(Q-LMI)的形式,给出了Q-LMI问题的基于LMI方法的求解步骤。为了使得Q-LMI问题有解,可引入一些LMI约束,提高了Q-LMI问题的可解性。基于Q-LMI条件,揭示了系统不确定参数界与系统控制规模的关系,提出了“不同的摄动实施不同规模的控制”的鲁棒能稳定的分层次控制策略。最后,通过一个例子说明了结论的可行性。

Robust stabilization for uncertain linear systems is studied using Lyapunov stability theory and linear matrix inequality approach. Parameter uncertainties under consideration are time-varying and norm-bounded. A sufficient condition for the existence of such a controller is established in a Q-LMI form, and the solution procedure of the Q-LMI problem is proposed. The solvability for the Q-LMI problem can be improved by adding some LMI constraints to the Q-LMI. Based on the Q-LMI condition, a robust stable layered control strategy for the robust stabilization, namely, 'different controller is acted on the system with different parameter perturbation', is presented. An example is given to illustrate the feasibility of the strategy.