Robust gain-scheduled control of linear parameter-varying systems with uncertain scheduling parameters in the presence of the time-invariant uncertainties

In this paper, a new approach is presented to design a gain-scheduled state-feedback controller for uncertain linear parameter-varying systems. It is supposed that the state-space matrices of them are the linear combination of the uncertain scheduling parameters. It is assumed that the existed uncertainties are of type of time-invariant parametric uncertainties with specified intervals. Simultaneous presence of the concepts of the gain-scheduling and the time-invariant uncertainties is a serious challenge. Because, the philosophy of the gain-scheduling is variability with time. But, the time-invariant parametric uncertainties are constant and unknown. To obviate this challenge, a robust state-feedback law is proposed that is robust against the time-invariant uncertainties. In this method, the arbitrary values are selected for the uncertainties from the defined intervals. But, the selected values are not necessarily equal to the true ones. Hence, the new scheduling parameters are presented to calculate the proposed controller. Finally, the proof of the proposed scheme is presented based on Lyapunov concept. To show the effectiveness of the final controller, the proposed method is simulated to stabilize the roll rate of a typical missile. Also, the simulation results are compared with the experimental ones in the presence of the INS (Inertial Navigation System) module.