Stabilizing a class of nonlinear parameter-varying systems using interval observer based on a piecewise framework

This article addresses an interval observer-based control for stabilizing a class of nonlinear parameter-varying systems with noisy output by designing a switching surface. An input-dependent interval observer is firstly developed to estimate the lower and upper bounds of the states. Next, a switching-based controller is designed to stabilize the interval observer which implies the stability of the main parameter-varying system. The developed stabilizing switching surfaces are designed based on the outputs of the main system and the bounds of the states of the observer. By choosing an appropriate piecewise Lyapunov function, the closed-loop stability analysis of the interval observer system leads to a set of linear matrix inequalities including stability and Metzler constraints, simultaneously. The effectiveness of the proposed method is verified using the simulation results.