Related papers: Comparison theorem for infinite-dimensional linear…
The problem of finite-dimensional asymptotics of infinite-dimensional dynamic systems is studied. A non-linear kinetic system with conservation of supports for distributions has generically finite-dimensional asymptotics. Such systems are…
The paper considers the design of a nonlinear dissipative impulsive observer based on non-periodic discrete-time measurements. Sufficient conditions are derived for (i) exponential convergence of the observer in absence of measurement…
This paper deals with the stability analysis problem of discrete-time switched linear systems with ranged dwell time. A novel concept called L-switching-cycle is proposed, which contains sequences of multiple activation cycles satisfying…
A susceptible, asymptomatic, infectious, quarantined, and hospitalized (SAIQH) compartmental model on time scales is introduced and a suitable Lyapunov function is defined. Main results include: the proof that the system is permanent; proof…
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…
The paper considers a general concept of dichotomy with different growth rates for linear discrete-time systems in Banach spaces. Characterizations in terms of Lyapunov type sequences of norms are given. The approach is illustrated by…
We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…
This paper studies the exponential stabilization on infinite dimensional system with impulse controls, where impulse instants appear periodically. The first main result shows that exponential stabilizability of the control system with a…
This paper considers discrete-time switched systems under dwell-time switching and in the presence of saturation nonlinearity. Based on Multiple Lyapunov Functions and using polytopic representation of nested saturation functions, a…
If a differential equation in a Banach manifold is invariant or quasi-invariant under the action of one or more Lie groups, then its stationary points cannot be isolated, so that classical linearized stability theorem does not apply to it.…
We present two linked theorems on passivity: the passive behavior theorem, parts 1 and 2. Part 1 provides necessary and sufficient conditions for a general linear system, described by a set of high order differential equations, to be…
This paper presents a synchronization criterion for networks of infinite-dimensional linear systems, extending a previous result for finite-dimensional systems. Our result, established in the general framework of input-output relations,…
In this paper, we investigate a class of stochastic impulsive fractional differential evolution equations with infinite delay in Banach space. Firstly sufficient conditions of the existence and uniqueness of the mild solution for this type…
We establish the asymptotic completeness in the nonlinear Lamb system for hyperbolic stationary states. For the proof we construct a trajectory of a reduced equation (which is a nonlinear nonautonomous ODE) converging to a hyperbolic…
This paper addresses the following classical question: giving a sequence of identically distributed random variables in the domain of attraction of a normal law, does the associated linear process satisfy the central limit theorem? We study…
We consider small nonlinear perturbations of linear systems on a time scale with the phase space being finite or infinite-dimensional. For $\Delta$-differential operators, corresponding to linear dynamic systems we consider their…
Motivated by a real problem in steel production, we introduce and analyze a general class of singularly perturbed linear hybrid systems with both switches and impulses, in which the slow or fast nature of the variables can be…
Many natural systems, such as neurons firing in the brain or basketball teams traversing a court, give rise to time series data with complex, nonlinear dynamics. We can gain insight into these systems by decomposing the data into segments…
In this paper we investigate four concepts of exponential stability for difference equations in Banach spaces. Characterizations of these concepts are given. They can be considered as variants for the discrete-time case of the classical…
We show that the dynamical symmetry exists in dissipative quantum many-body systems. Under constraints on both Hamiltonian and dissipation parts, the time evolution of particular observables can be symmetric between repulsive and attractive…