Input–Output Finite-Time Reliable Static Output Control of Time-Varying System With Input Delay

This paper investigates input-output finite-time reliable static output feedback (SOF) control of a time-varying system under the influence of both input time delay and actuator failures. An actuator fault model consisting of linear and nonlinear faults is considered during the time-varying control process. The objective is to design a reliable SOF controller that can ensure input-output finite-time stability (IO-FTS) of the resulting closed-loop system. An augmented time-varying Lyapunov functional is constructed, in which some Lyapunov matrices are variable function of time t. By dividing the time interval and delay interval into equal segments, the matrix-valued functions are expressed by a linear interpolation formula. Moreover, combining with the single and double Wirtinger-based integral inequalities, delay-dependent IO-FTS conditions are derived. It is shown that the SOF control issue is solved in forms of linear matrix inequalities. In the end, the effectiveness is demonstrated by simulations.

I. Introduction

The study on time-delay systems (TDSs) has a long history, since the existence of time delay is universal, for example, manufacturing processes, networked control systems, fluid transmissions, etc. Time delay may bring both negative and positive influences. It is usually a source of damage to systems’ performances [1]–[3]. Meanwhile, the time-delay phenomenon is helpful for the stabilization of some systems [4], [5]. Consequently, the study of TDSs has both practical value and theoretical significance [6]–[8]. Most results have been based on Lyapunov methods [9]. In [10], the Lyapunov–Krasovskii approach was used to stabilize the system with input time-delay for the first time. A discretized Lyapunov functional method was proposed in [11] and [12], in which a complete Lyapunov–Krasovskii functional (LKF) was constructed. It has been proven that this method is efficient and the obtained results are closed to analytical ones. Much literature about the study of TDSs adopted this method, for instance, [13] and [14].