Robust integral feedback control based on interval observer for stabilising parameter‐varying systems

Abstract

This study develops a novel method for designing a controller based on an interval observer to stabilise a class of non-linear parameter-varying systems. The interval observer, that provides estimates of lower and upper bounds on main states, is described in a non-affine piecewise form with states and inputs-dependent switching mechanisms. Non-affine piecewise model of interval observer is converted to an affine piecewise model by applying a state variable change. Then, by choosing an appropriate piecewise quadratic Lyapunov function, the control input is developed to stabilise the interval observer in all operating regions regarding input-to-state stability that leads to stabilisation of the system. The Lyapunov analysis is based on the subspace-partitions information and preserves the continuity of Lyapunov function in the boundaries of the regions. Compared with the existing interval observer-based control methods, the proposed method considers less conservative assumptions and can be applied to a much broader class of parameter-varying systems. The simulation results for several examples indicate the effectiveness of the proposed method.