Systems & Control Letters
Nonquadratic Lyapunov functions for robust control
Automatica (Journal of IFAC)
Design of Observers for Hybrid Systems
HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
Piecewise Linear Control Systems
Piecewise Linear Control Systems
Convex Optimization
Infinity norms as lyapunov functions for model predictive control of constrained PWA systems
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Brief Analysis of discrete-time piecewise affine and hybrid systems
Automatica (Journal of IFAC)
Brief On absolute stability analysis by polyhedral Lyapunov functions
Automatica (Journal of IFAC)
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This paper considers off-line synthesis of stabilizing static feedback control laws for discrete-time piecewise affine (PWA) systems. Two of the problems of interest within this framework are: (i) incorporation of the S-procedure in synthesis of a stabilizing state feedback control law and (ii) synthesis of a stabilizing output feedback control law. Tackling these problems via (piecewise) quadratic Lyapunov function candidates yields a bilinear matrix inequality at best. A new solution to these problems is proposed in this work, which uses infinity norms as Lyapunov function candidates and, under certain conditions, requires solving a single linear program. This solution also facilitates the computation of piecewise polyhedral positively invariant (or contractive) sets for discrete-time PWA systems.