91 research outputs found
Relative controllability of linear difference equations
In this paper, we study the relative controllability of linear difference
equations with multiple delays in the state by using a suitable formula for the
solutions of such systems in terms of their initial conditions, their control
inputs, and some matrix-valued coefficients obtained recursively from the
matrices defining the system. Thanks to such formula, we characterize relative
controllability in time in terms of an algebraic property of the
matrix-valued coefficients, which reduces to the usual Kalman controllability
criterion in the case of a single delay. Relative controllability is studied
for solutions in the set of all functions and in the function spaces and
. We also compare the relative controllability of the system for
different delays in terms of their rational dependence structure, proving that
relative controllability for some delays implies relative controllability for
all delays that are "less rationally dependent" than the original ones, in a
sense that we make precise. Finally, we provide an upper bound on the minimal
controllability time for a system depending only on its dimension and on its
largest delay
Stabilization of Persistently Excited Linear Systems by Delayed Feedback Laws
International audienceThis paper considers the stabilization to the origin of a persistently excited linear system by means of a linear state feedback, where we suppose that the feedback law is not applied instantaneously, but after a certain positive delay (not necessarily constant). The main result is that, under certain spectral hypotheses on the linear system, stabilization by means of a linear delayed feedback is indeed possible, generalizing a previous result already known for non-delayed feedback laws
On the gap between deterministic and probabilistic joint spectral radii for discrete-time linear systems
Given a discrete-time linear switched system associated
with a finite set of matrices, we consider the measures of its
asymptotic behavior given by, on the one hand, its deterministic joint spectral
radius and, on the other hand, its probabilistic
joint spectral radii for Markov random
switching signals with transition matrix and a corresponding invariant
probability . Note that is larger than or
equal to for every pair . In
this paper, we investigate the cases of equality of with either a single or with the
supremum of over and we aim at
characterizing the sets for which such equalities may occur
-asymptotic stability analysis of a 1D wave equation with a boundary nonmonotone damping
This paper is concerned with the asymptotic stability analysis of a one dimensional wave equation with a nonlinear non-monotone damping acting at a boundary. The study is performed in an -functional framework, . Some well-posedness results are provided together with exponential decay to zero of trajectories, with an estimation of the decay rate. The well-posedness results rely mainly on some results collected in [7]. Asymptotic behavior results are obtained by the use of a suitable Lyapunov functional if is finite and on a trajectory-based analysis if
Stability of non-autonomous difference equations with applications to transport and wave propagation on networks
International audienceIn this paper, we address the stability of transport systems and wave propagation on networks with time-varying parameters. We do so by reformulating these systems as non-autonomous difference equations and by providing a suitable representation of their solutions in terms of their initial conditions and some time-dependent matrix coefficients. This enables us to characterize the asymptotic behavior of solutions in terms of such coefficients. In the case of difference equations with arbitrary switching, we obtain a delay-independent generalization of the well-known criterion for autonomous systems due to Hale and Silkowski. As a consequence, we show that exponential stability of transport systems and wave propagation on networks is robust with respect to variations of the lengths of the edges of the network preserving their rational dependence structure. This leads to our main result: the wave equation on a network with arbitrarily switching damping at external vertices is exponentially stable if and only if the network is a tree and the damping is bounded away from zero at all external vertices but at most one
Persistently damped transport on a network of circles
International audienceIn this paper we address the exponential stability of a system of transport equations with intermittent damping on a network of circles intersecting at a single point . The equations are coupled through a linear mixing of their values at , described by a matrix . The activity of the intermittent damping is determined by persistently exciting signals, all belonging to a fixed class. The main result is that, under suitable hypotheses on and on the rationality of the ratios between the lengths of the circles, such a system is exponentially stable, uniformly with respect to the persistently exciting signals. The proof relies on an explicit formula for the solutions of this system, which allows one to track down the effects of the intermittent damping
On the gap between deterministic and probabilistic joint spectral radii for discrete-time linear systems
Given a discrete-time linear switched system associated with a finite set of matrices, we consider the measures of its asymptotic behavior given by, on the one hand, its deterministic joint spectral radius and, on the other hand, its probabilistic joint spectral radii for Markov random switching signals with transition matrix and a corresponding invariant probability . Note that is larger than or equal to for every pair . In this paper, we investigate the cases of equality of with either a single or with the supremum of over and we aim at characterizing the sets for which such equalities may occur
Approximate and exact controllability criteria for linear one-dimensional hyperbolic systems
This paper deals with the controllability of linear one-dimensional
hyperbolic systems. Reformulating the problem in terms of linear difference
equations and making use of infinite-dimensional realization theory, we obtain
both necessary and sufficient conditions for approximate and exact
controllability, expressed in the frequency domain. The results are applied to
flows in networks
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