一类非线性不确定中立时滞系统保性能控制

Guaranteed cost control for a class of nonlinear uncertain neutral systems with mixed delays

讨论了一类非线性不确定中立系统的保性能控制的问题,对于给定的性能函数及所容许的不确定和时滞,设计一个无记忆状态反馈控制律使得闭环系统是渐进稳定的,闭环系统的性能函数值不大于给定的一个数;利用-φProcedure lemma相对简单的解决了一类带有(B+ΔB(t))f(.)时变非线性扰动函数系统的无记状态反馈保性能控制律问题,最后应用线性矩阵不等式的方法给出了最优无记忆状态反馈保性能控制律的设计方法,并通过一个算例说明此方法的可行性.

A guaranteed control problem is studied on a class of nonlinear uncertain neutral systems. Attention is focused on the design of nomemory state feedback controllers such that the closed-loop systerm is as mptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainty and time delay. One major contribution of the present work is that the solvability of design of nomemory state feedback controllers for a class of systems with （ B＋B（t））f（· ） time-varying nonlinear perturbations functions is easily obtained by φ-Procedure lemma. At last, the existence of suboptional nomemory state feedback guaranteed cost controller is derived in term of LMIs. A example is used to illutrate the feasibility of the design procedure.