Explicit robustness margin for contractive piecewise affine control laws

Rajesh Koduri (1) , Pedro Rodriguez-Ayerbe (1) , Sorin Olaru (2, 1) , Morten Hovd (3)

1 L2S - Laboratoire des signaux et systèmes
2 DISCO - Dynamical Interconnected Systems in COmplex Environments
3 ITK NTNU - Department of Engineering Cybernetics [Trondheim]

—This paper deals with the class of discrete-time linear dynamics affected by polytopic uncertainty in closed loop with contractive piecewise affine (PWA) control law. Starting from the hypothesis that the synthesis ensures a λ-contractive PWA control law for the nominal model, the objective is to calculate the robustness margin guaranteeing the contractivity (and consequently the asymptotic stability) of the closed loop dynamics. The robustness margin is represented as a subset of parameters within the set describing the polytopic uncertainty. For all these parameters, the λ-contractive behavior of the trajectories can be certified. This set of parameters is then compared to the set assuring the invariance of the considered closed-loop PWA dynamics which represents a limit case of the robustness study presented here.

Domains: Automatic

Rajesh Koduri, Pedro Rodriguez-Ayerbe, Sorin Olaru, Morten Hovd. Explicit robustness margin for contractive piecewise affine control laws. 20th International Conference on System Theory, Control and Computing (ICSTCC), Oct 2016, Sinaia, Romania. pp.806 - 811, ⟨10.1109/ICSTCC.2016.7790767⟩. ⟨hal-01429250⟩