Related papers: Uniform Detectability of Linear Time Varying Syste…
This work proposes a detectability condition for linear time-varying systems based on the exponential dichotomy spectrum. The condition guarantees the existence of an observer, whose gain is determined only by the unstable modes of the…
The objective of this paper is to study detectability, observability and related Lyapunov-type theorems of linear discrete-time time-varying stochastic systems with multiplicative noise. Some new concepts such as uniform detectability,…
In this paper we consider some concepts of exponential splitting for nonautonomous linear discrete-time systems. These concepts are generalizations of some well-known concepts of (uniform and nonuniform) exponential dichotomies. Connections…
The existence of exponential dichotomies has been well-established as a powerful tool to study existence, stability, and bifurcations of coherent structures. Currently, the application of exponential dichotomies to elliptic problems posed…
This paper proposes a unified approach for studying global exponential stability of a general class of switched systems described by time-varying nonlinear functional differential equations. Some new delay-independent criteria of global…
This paper discusses stability and robustness properties of a recently proposed observer algorithm for linear time varying systems. The observer is based on the approximation and subsequent modification of the non-negative Lyapunov…
In this paper it is showed that if a time-varying uncertain system is robustly completely detectable then there exists an estimator for this system, i.e. we can estimate asymptotically the state vector of the system. Moreover, if a…
Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…
In this paper, we provide a necessary and sufficient condition ensuring the property of exponential dichotomy for periodic linear systems of generalized differential equations. This condition allow us to revisit a recent result of…
The aim of this paper is to extend the concept of regional exponential general observability to the case of Neumann boundary conditions problem in diffusion system. More precisely, for linear distributed parameter diffusion systems, we show…
In this paper we propose a new observability property for nonautonomous linear control systems in finite dimension: the nonuniform complete observability, which is more general than the uniform complete observability. A dual relationship is…
The robustness property of exponential dichotomies refers to the stability of this notion under small linear perturbations. In recent work~\cite{PPX}, the authors have identified a new class of perturbations under which the notion of a…
We examine robustness of exponential dichotomies of boundary value problems for general linear first-order one-dimensional hyperbolic systems. The boundary conditions are supposed to be of types ensuring smoothing solutions in finite time,…
While the asymptotic stability of positive linear systems in the presence of bounded time delays has been thoroughly investigated, the theory for nonlinear positive systems is considerably less well-developed. This paper presents a set of…
We define observability and detectability for linear switching systems as the possibility of reconstructing and respectively of asymptotically reconstructing the hybrid state of the system from the knowledge of the output for a suitable…
We prove that for every discrete-time linear switching system in two complex variables and with finitely many switching states, either the system is Lyapunov stable or there exists a trajectory which escapes to infinity with at least linear…
In this paper, ordinary and exponential dichotomies are defined in differential equations with equations with piecewise constant argument of general type. We prove the asymptotic equivalence between the bounded solutions of a linear system…
Building on the recent notion of non-uniform complete observability, and on the fact that this property ensures non-uniform exponential detectability, this paper establishes the converse implication under suitable additional assumptions.…
The method to design exponentially stable adaptive observers is proposed for linear time-invariant systems parameterized by unknown physical parameters. Unlike existing adaptive solutions, the system state-space matrices A, B are not…
In this paper we deal with infinite-dimensional nonlinear forward complete dynamical systems which are subject to external disturbances. We first extend the well-known Datko lemma to the framework of the considered class of systems. Thanks…