14 research outputs found
A nonconservative LMI condition for stability of switched systems with guaranteed dwell time
Ensuring stability of switched linear systems with a guaranteed dwell time is an important problem in control systems. Several methods have been proposed in the literature to address this problem, but unfortunately they provide sufficient conditions only. This technical note proposes the use of homogeneous polynomial Lyapunov functions in the non-restrictive case where all the subsystems are Hurwitz, showing that a sufficient condition can be provided in terms of an LMI feasibility test by exploiting a key representation of polynomials. Several properties are proved for this condition, in particular that it is also necessary for a sufficiently large degree of these functions. As a result, the proposed condition provides a sequence of upper bounds of the minimum dwell time that approximate it arbitrarily well. Some examples illustrate the proposed approach. © 2012 IEEE.published_or_final_versio
Computing upper-bounds of the minimum dwell time of linear switched systems via homogenous polynomial lyapunov functions
Regular Session - Switched Systems IIThis paper investigates the minimum dwell time for switched linear systems. It is shown that a sequence of upper bounds of the minimum dwell time can be computed by exploiting homogeneous polynomial Lyapunov functions and convex optimization based on LMIs. This sequence is obtained by adopting two possible representations of homogeneous polynomials, one based on Kronecker products, and the other on the square matrix representation. Some examples illustrate the use and the potentialities of the proposed approach.published_or_final_versionThe 2010 American Control Conference (ACC), Baltimore, MD., 30 June-2 July 2010. In Proceedings of the American Control Conference, 2010, p. 2487-249
A Gel'fand-type spectral radius formula and stability of linear constrained switching systems
Using ergodic theory, in this paper we present a Gel'fand-type spectral
radius formula which states that the joint spectral radius is equal to the
generalized spectral radius for a matrix multiplicative semigroup \bS^+
restricted to a subset that need not carry the algebraic structure of \bS^+.
This generalizes the Berger-Wang formula. Using it as a tool, we study the
absolute exponential stability of a linear switched system driven by a compact
subshift of the one-sided Markov shift associated to \bS.Comment: 16 pages; to appear in Linear Algebra and its Application
Growth rates for persistently excited linear systems
We consider a family of linear control systems where
belongs to a given class of persistently exciting signals. We seek
maximal -uniform stabilisation and destabilisation by means of linear
feedbacks . We extend previous results obtained for bidimensional
single-input linear control systems to the general case as follows: if the pair
verifies a certain Lie bracket generating condition, then the maximal
rate of convergence of is equal to the maximal rate of divergence of
. We also provide more precise results in the general single-input
case, where the above result is obtained under the sole assumption of
controllability of the pair
A characterization of switched linear control systems with finite L 2 -gain
Motivated by an open problem posed by J.P. Hespanha, we extend the notion of
Barabanov norm and extremal trajectory to classes of switching signals that are
not closed under concatenation. We use these tools to prove that the finiteness
of the L2-gain is equivalent, for a large set of switched linear control
systems, to the condition that the generalized spectral radius associated with
any minimal realization of the original switched system is smaller than one