A Systematic LMI Approach to Design Multivariable Sliding Mode Controllers

TL;DR

This paper presents a systematic LMI-based method for designing multivariable sliding mode controllers that ensure finite-time stability and optimize reaching time for uncertain systems.

Contribution

It introduces a systematic LMI framework for designing robust multivariable sliding mode controllers with finite-time stability guarantees.

Findings

LMI conditions ensure global stability of the closed-loop system.

Convex optimization minimizes reaching time based on initial conditions.

Examples demonstrate the effectiveness of the proposed control design.

Abstract

This paper deals with sliding mode control for multivariable polytopic uncertain systems. We provide systematic procedures to design variable structure controllers (VSCs) and unit-vector controllers (UVCs). Based on suitable representations for the closed-loop system, we derive sufficient conditions in the form of linear matrix inequalities (LMIs) to design the robust sliding mode controllers such that the origin of the closed-loop system is globally stable in finite time. Moreover, by noticing that the reaching time depends on the initial condition and the decay rate, we provide convex optimization problems to design robust controllers by considering the minimization of the reaching time associated with a given set of initial conditions. Two examples illustrate the effectiveness of the proposed approaches.