一类不确定非线性离散时滞系统的鲁棒镇定问题

Robust Stabilization of Nonlinear Discrete-time Systems with Uncertain Parameters

研究了不确定非线性离散系统的鲁棒镇定问题,把不确定非线性离散系统的鲁棒镇定问题转化为严格的线性矩阵不等式,给出了可设计系统无记忆状态反馈控制律的充分条件;当条件满足时设计出无记忆状态反馈控制律使闭环系统渐近稳定,同时得到有界非线性扰动项的最大界值.然后把结果推广到非线性时滞系统,得到了相应的结果.

The problem of robust stabilization of nonlinear discrete-time systems with uncertain parameters is discussed. The parameter uncertainties are assumed to be time-invariant and normbounded. Through a strict linear matrix inequality（LMI） ,a sufficient condition is provided for designing a memoryless state feedback controller which guarantees the stability of the closed-loop systems and at the same time maximizes the bound on the non-linearity. In the end,the result is extended to nonlinear time-delay systems.