Flexible-Step MPC for Switched Linear Systems With No Quadratic Common Lyapunov Function

IEEE Transactions on Automatic Control, vol. 70, pp. 6316–6322

Abstract

In this paper, we develop a systematic method for constructing a generalized discrete-time control Lyapunov function for the flexible-step Model Predictive Control (MPC) scheme, recently introduced in [2], when restricted to the class of linear systems. Specifically, we show that a set of Linear Matrix Inequalities (LMIs) can be used for this purpose, demonstrating its tractability. The main consequence of this LMI formulation is that, when combined with flexible-step MPC, we can effectively stabilize switched control systems, for which no quadratic common Lyapunov function exists.

Authors 3

1. Annika Fürnsinn

   Queen's University

   Affiliation as printed

   Department of Mathematics and Statistics, Queen's University, Kingston, ON, Canada

   Department of Mathematics and Statistics, Queen's University, Kingston, Canada

2. Christian Ebenbauer Aachen Chair of Intelligent Control Systems

   RWTH Aachen University

   Affiliation as printed

   Chair of Intelligent Control Systems, RWTH Aachen University, Aachen, Germany

3. Bahman Gharesifard

   Queen's University

   Affiliation as printed

   Department of Mathematics and Statistics, Queen's University, Kingston, ON, Canada

   Department of Mathematics and Statistics, Queen's University, Kingston, Canada