We consider the asymptotic behavior of solutions of a linear differential system x D A.t/x, where A is continuous on an interval Œa;1/. We are interested in the situation where the system may not have a desirable asymptotic property such as stability, strict stability, uniform stability, or linear asymptotic equilibrium, but its solutions can be written as x D Pu, where P is continuously differ...

We consider the problem of asymptotic reconstruction of the state and parameter values for dynamical systems that cannot be transformed into the canonical adaptive observer form. A solution to this problem is proposed for a class of systems for which the unknowns are allowed to be nonlinearly parameterized functions of state and time. Going beyond asymptotic Lyapunov stability, we provide for t...

We consider the problem of asymptotic reconstruction of the state and parameter values for dynamical systems that cannot be transformed into the canonical adaptive observer form. A solution to this problem is proposed for a class of systems for which the unknowns are allowed to be nonlinearly parameterized functions of state and time. Going beyond asymptotic Lyapunov stability, we provide for t...

When defining a differential operator, one often employs, besides ordinary derivatives, generalized derivatives, which appear in a natural way when considering extensions of differential operators defined on differentiable functions, and weak derivatives, related to the transition to the adjoint operator [9]. Derivatives of fractional and negative orders appear when the differentiation is defin...

A subset A of the state space is called uniformly globally weakly attractive if for any neighborhood S of A and any bounded subset B there is a uniform finite time τ so that any trajectory starting in B intersects S within the time not larger than τ . We show that practical uniform global asymptotic stability (pUGAS) is equivalent to the existence of a bounded uniformly globally weakly attracti...

Abstract. This paper presents sufficient conditions which guarantee that the equilibrium of the damped harmonic oscillator x′′ + h(t)x′ + ωx = 0 is uniformly asymptotically stable, where h : [0,∞) → [0,∞) is locally integrable. These conditions work to suppress the rapid growth of the frictional force expressed by the integral amount of the damping coefficient h. The obtained sufficient conditi...

In this present note, we formulate a model for hybrid dynamical systems with delay, which covers a large class of delay systems. Under several mild assumptions, we establish sufficient conditions for uniform asymptotic stability of hybrid dynamical systems with delay via Lyapunov–Razumikhin technique. To demonstrate the developed theory, we conduct stability analyzes for delay sampled-data feed...

In this paper the notions of non-uniform in time robust global asymptotic output stability (RGAOS) and input-to-output stability (IOS) for discrete-time systems are studied. Characterizations as well as links between these notions are provided. Particularly, it is shown that a discrete-time system with continuous dynamics satisfies the non-uniform in time IOS property if and only if the corresp...