Stabilizing a class of parameter-varying systems using interval observer-based controller

The aim of this paper is to propose a novel method for controlling a class of parameter-varying systems by controlling interval observer. The interval observers, that are applicable for the systems with uncertainty, estimate bounds on the states instead of estimating the states. It has been shown that by designing appropriate control inputs for controlling the bounds of the interval observer, the states of the system can be also controlled using the same control inputs. For this purpose, a suitable interval observer is firstly designed for the parameter-varying system and the required conditions, for which the dynamical system consisting of lower and upper bounds on error is monotone, are presented. Then, a novel controller is designed for stabilizing the interval observer such that the bounds on the states are stabilized and thereby the states are also stabilized. The proposed controller is based on adaptive sliding mode control method that is utilized to tackle the effects of variations in some parameters of the interval observers as well as the existing disturbances in the system. By choosing an appropriate Lyapunov function, the conditions and areas for the stability of the observer are determined. Simulation results, obtained by applying the method to a sample system, show the effectiveness of the proposed method.