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This technical report presents a direct proof of Theorem~1 in [1] and some consequences that also account for (20) in [1]. This direct proof exploits a state space change of basis which replaces the coupled difference equations (10) in [1]…
By applying a Mawhin's continuation theorem of coincidence degree theory, we establish sufficient conditions for the existence of a periodic solution for a class of impulsive neutral differential equations. The procedure adopted in this…
In this paper, we investigate a class of hybrid stochastic heat equations. By explicit formulae of solutions, we not only reveal the sample Lyapunov exponents but also discuss the $p$th moment Lyapnov exponents. Moreover, several examples…
Time-varying ISS-Lyapunov functions for impulsive systems provide a necessary and sufficient condition for ISS. This property makes them a more powerful tool for stability analysis than classical candidate ISS-Lyapunov functions providing…
We prove that impulsive systems, which possess an ISS Lyapunov function, are ISS for impulse time sequences, which satisfy the fixed dwell-time condition. If the ISS Lyapunov function is the exponential one, we provide stronger result,…
Small perturbation of the Liouville equation under singular initial data is considered. An asymptotics of the singular solution is constructed by the method which is similar to Bogolubov -- Krylov one. The main object is an asymptotics of…
The robust tracking and model following problem of linear discrete-time systems is investigated in this paper. An approach to design robust tracking controllers is proposed. The system is controlled to track dynamic inputs generated from a…
This is a survey of known results on estimating the principal Lyapunov exponent of a time-dependent linear differential equation possessing some monotonicity properties. Equations considered are mainly strongly cooperative systems of…
The present research paper is devoted to investigate the existence, uniqueness of mild solutions for impulsive delay integrodifferential equations with integral impulses in Banach spaces. We also investigate the dependence of solutions on…
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…
Stability analysis plays a crucial role in studying the behavior of dynamical systems with theoretical and engineering applications. Among various kinds of stability, the stability of equilibrium points is of the greatest importance which…
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 introduce for the first time a class of state-dependent maximal monotone differential inclusions. Then the existence and uniqueness of solutions are obtained by using an implicit discretization scheme and a kind of…
Switched linear hyperbolic partial differential equations are considered in this paper. They model infinite dimensional systems of conservation laws and balance laws, which are potentially affected by a distributed source or sink term. The…
We study the concentration phenomenon for discrete-time random dynamical systems with an unbounded state space. We develop a heuristic approach towards obtaining exponential concentration inequalities for dynamical systems using an entirely…
We study the systems of ordinary differential equations which are implicit with respect to the higher derivatives, appearing in the linear form, and their solutions near the singular points. The invertibility of the higher derivatives…
In this paper, we investigate existence and uniqueness of solutions of nonlinear Volterra-Fredholm impulsive integrodifferential equations. Utilizing theory of Picard operators we examine data dependence of solutions on initial conditions…
Every irreducible discrete-time linear switching system possesses an invariant convex Lyapunov function (Barabanov norm), which provides a very refined analysis of trajectories. Until recently that notion remained rather theoretical apart…
We obtain global and local theorems on the existence of invariant manifolds for perturbations of non autonomous linear difference equations assuming a very general form of dichotomic behavior for the linear equation. The results obtained…
In this paper we consider a singular wave equation with distributional and more singular non-distributional coefficients and develop tools and techniques for the phase-space analysis of such problems. In particular we provide a detailed…