Finite time dissipativity-based reliable control for time-varying system with delay and linear fractional uncertainties

This paper is concerned with the problem of finite time dissipativity-based reliable control for a time-varying system with linear fractional uncertainty (LFU) and time delay. An actuator fault model consisting of both linear and nonlinear faults is considered during the time-varying control process. By implementing an augmented time-varying Lyapunov functional and using the Wirtinger-type integral inequality, delay-dependent finite time dissipative conditions are established in forms of derivative linear matrix inequalities (DLMIs), which can guarantee the closed-loop system is finite time dissipative for all admissible uncertainties. Then, the DLMIs are transformed into a series of recursive linear matrix inequalities (RLMIs) based on the discretization method. And an algorithm is given to solve the RLMIs to obtain the state feedback gain. Simulation results demonstrate the validity of the proposed approach.