Reliable Guaranteed Cost Control of Uncertain Systems with Nonlinear Perturbations

Network control system (NCS) is a distributed real-time feedback control system with the continuous development of network technology. It is generally composed of network, controller, actuator and sensor. It has brought great convenience to people in many fields, but it also has many problems, which makes the research of control system more complicated. Recently, there have been some efforts to tackle the reliable guaranteed cost controller design problem, and some good results have also been obtained for the continuous-time and for the discrete-time. However, there have been few results in the literature of an investigation for the reliable guaranteed cost controller design of nonlinear uncertain systems with time-varying state delay and actuator failure. This paper concerns the reliable guaranteed cost control problem of uncertain systems with time-varying state delay and nonlinear perturbations for a given quadratic cost function. The problem is to design a reliable guaranteed cost state feedback control law which can tolerate actuator failures, such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound. Firstly, the existence condition of reliable guaranteed cost control law is given by constructing Lyapunov stability function and using linear matrix inequality (LMI). Secondly, the design method of the optimal reliable guaranteed cost controller is given by solving the convex optimization problem with LMI constraints, which minimizes the upper bound of guaranteed cost for closed-loop systems. In the end, the numerical simulation result illustrates the effectiveness of the proposed method.