Robust saturation controller for linear time-invariant system with structured real parameter uncertainties

Abstract

This paper is focused on a robust saturation controller for the linear time-invariant (LTI) system involving both actuator's saturation and structured real parameter uncertainties. The controller suggested in this paper can analytically prescribe the upper and lower bounds of parameter uncertainties, and guarantee the closed-loop robust stability of the system in the presence of actuator's saturation. The suboptimal bang–bang control method is extended to LTI system with parameter uncertainties. Based on affine quadratic stability and multi-convexity concept, the robust optimal bang–bang controller is newly derived by minimizing the time derivative of affine Lyapunov function subjected to the limit of control force. Since this controller is a gain-scheduled type, it requires the exact knowledge of uncertain parameters. Another robust saturation controller with a fixed gain is proposed and the linear matrix inequality ( LMI)- based sufficient existence conditions for a fixed-gain controller are derived. The effectiveness and the availability of the proposed controller are investigated by a practical numerical example. Through numerical simulations, it is confirmed that the proposed robust saturation controller is robustly stable with respect to parameter uncertainties over the prescribed range defined by the upper and lower bounds.