Attractive Ellipsoids in Sliding Mode Control

Abstract

In this chapter, a new sliding mode control design algorithm for a linear and a class of nonlinear quasi-Lipschitz disturbed systems is presented. It is based on the appropriate selection of a sliding surface via the invariant ellipsoid method. The designed control guarantees minimization of unmatched disturbance effects to system motions in a sliding mode. The theoretical results are verified by numerical simulations. Additionally, a methodology for the design of sliding mode controllers for linear systems subjected to matched and unmatched perturbations is proposed. It is considered that the control signal is applied through a first-order low-pass filter. The technique is based on the existence of an attracting (invariant) ellipsoid such that the convergence to a quasiminimal region of the origin using the suboptimal control signal is guaranteed. The design procedure is given in terms of the solution of a set of matrix inequalities. Benchmark examples illustrating the design are given.