Non-overshooting output shaping for switched linear systems under arbitrary switching using eigenstructure assignment

TL;DR

This paper presents a control design method for switched linear MIMO systems that guarantees global stability and non-overshooting output tracking through eigenstructure assignment, applicable under arbitrary switching signals.

Contribution

It introduces a novel eigenstructure assignment approach for switched MIMO systems that ensures stability and non-overshooting output tracking, with a constructive algorithm and feasibility conditions.

Findings

The method guarantees global asymptotic stability.

It achieves non-overshooting output tracking.

The approach is validated with numerical examples.

Abstract

We consider the analytical control design for a pair of switched linear multiple-input multiple-output (MIMO) systems that are subject to arbitrary switching signals. A state feedback controller design method is proposed to obtain an eigenstructure assignment that ensures that the closed-loop switched system is globally asymptotically stable, and the outputs achieve the non-overshooting tracking of a step reference. Our analysis indicates whether non-overshooting or even monotonic tracking is achievable for the given system and considered outputs and provides a choice of possible eigenstructures to be assigned to the constituent subsystems. We derive a structural condition that verifies the feasibility of the chosen assignment. A constructive algorithm to obtain suitable feedback matrices is provided, and the method is illustrated with numerical examples.