912 research outputs found
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 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
On convergence of infinite matrix products with alternating factors from two sets of matrices
We consider the problem of convergence to zero of matrix products
with factors from two sets of matrices,
and , due to a suitable choice of
matrices . It is assumed that for any sequence of matrices
there is a sequence of matrices such that the
corresponding matrix product converges to zero.
We show that in this case the convergence of the matrix products under
consideration is uniformly exponential, that is, , where the constants and
do not depend on the sequence and the corresponding sequence
.Comment: 7 pages, 13 bibliography references, expanded Introduction and
Section 4 "Remarks and Open Questions", accepted for publication in Discrete
Dynamics in Nature and Societ
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
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