Anti-windup strategies for discrete-time switched systems subject to input saturation

abstract

This paper deals with the design of anti-windup compensator for discrete-time switched systems subject to input saturation. The cases of static and dynamic anti-windup controllers are addressed aiming at maximising the estimate of the basin of attraction of the origin for the closed-loop system. Two aspects of the switching law are taken into account during the design: either it is arbitrary or it is a part of the complete control law. Theoretical conditions allowing to synthesise the anti-windup compensator are mainly described through linear matrix inequalities. Computational oriented conditions are then provided to solve convex optimisation problems that are able to give a constructive solution.

Keywords:

• Switched systems
• anti-windup
• Lyapunov functions
• saturation
• deadzone
• Lyapunov–(Metzler) inequalities

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by ANR project ArHyCo, Programme “Systèmes Embarqués et Grandes Infrastructures” – ARPEGE [contract number ANR-2008 SEGI 004 01-30011459], by ANR COMPACS – “Computation Aware Control Systems” [ANR-13-BS03-004] and by the European Community's Seventh Framework Programme (FP7/2007-2013) [grant number 257462]: HYCON2 Network of Excellence “Highly-Complex and Networked Control Systems” and finally by Région Lorraine.