Graph-based conditions for feedback stabilization of switched and LPV

This paper presents novel stabilizability conditions for switched linear systems with arbitrary and uncontrollable underlying switching signals. We distinguish and study two particular settings: (i) the robust case, in which the active mode is completely unknown and unobservable, and (ii) the modedependent case, in which the controller depends on the current active switching mode. The technical developments are based on graph-theory tools, relying in particular on the path-complete Lyapunov functions framework. The main idea is to use directed and labeled graphs to encode Lyapunov inequalities to design robust and mode-dependent piecewise linear state-feedback controllers. This results in novel and flexible conditions, with the particular feature of being in the form of linear matrix inequalities (LMIs). Our technique thus provides a first controller-design strategy allowing piecewise linear feedback maps and piecewise quadratic (control) Lyapunov functions by means of semidefinite programming. Numerical examples illustrate the application of the proposed techniques, the relations between the graph order, the robustness, and the performance of the closed loop. (c) 2023 Elsevier Ltd. All rights reserved.

Automated summary

This paper presents new stabilizability conditions for switched linear systems with arbitrary and uncontrollable underlying switching signals. The study focuses on two specific settings: the robust case with completely unknown and unobservable active mode, and the mode-dependent case with controller depending on the current active switching mode. The technical developments are based on graph-theory tools and path-complete Lyapunov functions framework, enabling the design of robust and mode-dependent piecewise linear state-feedback controllers using directed and labeled graphs.