Observer-Based Control for Continuous-Time Switched Linear Parameter-Varying Systems

This paper deals with the interval observer-based controller design for switched linear parameter-varying (LPV) systems with external disturbance and measurement noise. Firstly, with the help of positive system theory, we design asymptotic interval observers for the subsystems by giving the upper and the lower bounds of the disturbance and the measurement noise. Compared to the traditional observers, interval observers can manage with uncertainties better and provide the upper and the lower bounds for the state variables at any instant. Then, based on the new variable replacement method and multiple Lyapunov function method, we design an interval observer-based controller for the switched LPV systems and some sufficient conditions are obtained to guarantee the exponential stability of the closed-loop systems. Next, the corresponding solvability criteria for the interval observer-based controller are formulated. Finally, we provide a numerical example to illustrate the validity of the proposed results.