9 research outputs found
On the convergence of linear switched systems
International audienceThis paper investigates sufficient conditions for the convergence to zero of the trajectories of linear switched systems. We provide a collection of results that use weak dwell-time, dwell-time, strong dwell-time, permanent and persistent excitation hypothesis. The obtained results are shown to be tight by counterexample. Finally, we apply our result to the three-cell converter
Convergence Rate of Nonlinear Switched Systems
This paper is concerned with the convergence rate of the solutions of
nonlinear switched systems. We first consider a switched system which is
asymptotically stable for a class of inputs but not for all inputs. We show
that solutions corresponding to that class of inputs converge arbitrarily
slowly to the origin. Then we consider analytic switched systems for which a
common weak quadratic Lyapunov function exists. Under two different sets of
assumptions we provide explicit exponential convergence rates for inputs with a
fixed dwell-time
Geometry of the Limit Sets of Linear Switched Systems
The paper is concerned with asymptotic stability properties of linear
switched systems. Under the hypothesis that all the subsystems share a non
strict quadratic Lyapunov function, we provide a large class of switching
signals for which a large class of switched systems are asymptotically stable.
For this purpose we define what we call non chaotic inputs, which generalize
the different notions of inputs with dwell time. Next we turn our attention to
the behaviour for possibly chaotic inputs. To finish we give a sufficient
condition for a system composed of a pair of Hurwitz matrices to be
asymptotically stable for all inputs
Stability of uniformly bounded switched systems and Observability
This paper mainly deals with switched linear systems defined by a pair of
Hurwitz matrices that share a common but not strict quadratic Lyapunov
function. Its aim is to give sufficient conditions for such a system to be
GUAS.We show that this property of being GUAS is equivalent to the uniform
observability on of a bilinear system defined on a subspace whose
dimension is in most cases much smaller than the dimension of the switched
system.Some sufficient conditions of uniform asymptotic stability are then
deduced from the equivalence theorem, and illustrated by examples.The results
are partially extended to nonlinear analytic systems
Interval observers design for continuous-time linear switched systems
International audienceThis paper is devoted to investigate interval observers design for linear switched systems. The considered systems are subject to disturbances which are assumed to be unknown but bounded. First, observer gains are computed to ensure the stability of the estimation error. Then, under some changes of coordinates an interval observer is designed. Efficiency of the proposed method is demonstrated through a numerical example