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.