On feedback stabilization of linear switched systems via switching signal control

Motivated by recent applications in control theory, we study the feedback stabilizability of switched systems, where one is allowed to chose the switching signal as a function of $x(t)$ in order to stabilize the system. We propose new algorithms and analyze several mathematical features of the problem which were unnoticed up to now, to our knowledge. We prove complexity results, (in-)equivalence between various notions of stabilizability, existence of Lyapunov functions, and provide a case study for a paradigmatic example introduced by Stanford and Urbano.Comment: 19 pages, 3 figure

Necessary and sufficient condition for stabilizability of discrete-time linear switched systems: a set-theory approach

International audienceIn this paper, the stabilizability of discrete-time linear switched systems is considered. Several sufficient conditions for stabilizability are proposed in the literature, but no necessary and sufficient. The main contributions are the necessary and sufficient conditions for stabilizability based on set-theory and the characterization of a universal class of Lyapunov functions. An algorithm for computing the Lyapunov functions and a procedure to design the stabilizing switching control law are provided, based on such conditions. Moreover a sufficient condition for non-stabilizability for switched system is presented. Several academic examples are given to illustrate the efficiency of the proposed results. In particular, a Lyapunov function is obtained for a system for which the Lyapunov-Metzler condition for stabilizability does not hold

Stabilizability Analysis of Multiple Model Control with Probabilistic: Stabilizability Analysis of Multiple Model Control with Probabilistic

In this paper, we derive some useful necessary conditions for stabilizability of multiple model control using a bank of stabilizing state feedback controllers. The outputs of this set are weighted by their probabilities as a soft switching system and together fed back to the plant. We study quadratic stabilizability of this closed loop soft switching system for both continuous and discrete-time hybrid system. For the continuous-time hybrid system, a bound on sum of eigenvalues of  is found when their derivatives of Lyapunov functions are upper bounded.  For discrete-time hybrid system, a new stabilizability condition of soft switching signals is presented