Fault-alarm based hybrid control design for uncertain periodic piecewise time-varying systems with actuator constraints

This paper is concerned with the stabilization problem for continuous-time periodic piecewise time-varying uncertain systems with time-varying delay, actuator failures and external disturbances. Specifically, the actuator failure consists of both unknown actuator partial failure and actuator bias failure. Based on multiple threshold values, in this work, a fault-alarm based hybrid control protocol is developed, which is used to switch between robust and reliable controllers accurately and timely by eliminating false alarms. To be precise, a set of sufficient stability criteria is established in the form of linear matrix inequalities (LMIs) by considering an appropriate Lyapunov-Krasovskii functional with time-varying periodic piecewise positive-definite matrices. Furthermore, the desired time-varying robust and reliable controller gain matrices can be reckoned based on developed LMI-based constraints. Eventually, two numerical examples are presented, which include the mass-spring damper systems, to show the superiority and practicability of the designed controller.