一类不确定动态时滞系统的无记忆鲁棒镇定控制

MEMORYLESS ROBUST STABILIZATION OF A CLASS OF UNCERTAIN LINEAR TIME-DELAY SYSTEMS

针对状态和控制均存在滞后，同时具有未知且有界的一类时变不确定线性时滞系统，提出了一种无记忆鲁棒镇定控制器设计算法．给出了闭环系统二次稳定的充分条件，并利用一等价线性时不变系统的Ｈ∞标准问题综合方法来构造出所需的线性状态反馈控制律，即可通过求解一代数Ｒｉｃｃａｔｉ型方程来求得控制律静态增益阵，从而保证了解的存在性和可解性．

This paper presents a controller for robust stabilization of a class of uncertain linear dynamic systems with time-delays in both state and control. The uncertain systems under consideration are described by state differential equations which depend on time-varying unknown-but-bounded uncertain parameters. The sufficient conditions for quadratic stability of closed-loop systems are derived. The desired linear state feedback control law can be constructed by synthesis of an H∞ standard problem of equivalent linear time-invariant systems. That is to say, the static controller gain can be obtained by solving an algebraic Riccati equation, and thus the existence and feasibility of solution can be ensured.