一类非线性不确定时滞系统的可靠H^∞控制

Reliable H∞ Control for a Class of Nonlinear Uncertain Time-Delay Systems

研究了一类非线性不确定动态时滞系统的鲁棒可靠 H∞ 控制问题 ,其中状态矩阵和状态迟延矩阵的参数不确定性是范数有界的 ,模型的非线性不确定性是增益有界的 ,而它们无需满足匹配条件 .基于 Lyapunov稳定性理论导出了执行器失效情形下的可靠 H∞控制器存在的充分条件 ,通过求解一个线性矩阵不等式 (LMI)来设计控制律 .文中算例验证了该设计方法的有效性 .

This paper dealt with the problem of reliable H∞ control for a class of uncertain nonlinear systems with state delays. The parameter uncertainties in state matrix and state-delayed matrix were assumed to be norm-bounded, and the nonlinear uncertainties for plant were assumed to satisfy the gain boundedness condition. They need not satisfy any matching condition. Based on Lyapunov stability theory, a sufficient condition for existence of reliable H∞ controllers under actuator failures was derived. By solving a linear matrix inequality, the state feedback control laws were obtained. A numeric example is given to demonstrate the effectiveness of the design method.