Related papers: Lyapunov characterization of boundedness of reacha…
In this paper, we extend well-known relationships between global asymptotic controllability, sample stabilizability, and the existence of a control Lyapunov function to a wide class of control systems with unbounded controls, which includes…
We prove a converse Lyapunov theorem for almost sure stabilizability and almost sure asymptotic stabilizability of controlled diffusions: given a stochastic system a.s. stochastic open loop stabilizable at the origin, we construct a lower…
We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable…
We present an approach to approximate reachable sets for linear systems with bounded L-infinity controls in finite time. Our first approach investigates the boundaries of these sets and reveals an exact characterization for single-input,…
Converse optimality theory addresses an optimal control problem conversely where the system is unknown and the value function is chosen. Previous work treated this problem both in continuous and discrete time and non-extensively considered…
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…
The topic of this manuscript is the stability analysis of continuous-time switched nonlinear systems with constraints on the admissible switching signals. Our particular focus lies in considering signals characterized by upper and lower…
The classical global linearization theorem for autonomous system given in [C. Pugh, Amer. J. Math., 91 (1969) 363-367] requires that nonlinear system with hyperbolicity satisfies boundedness and Lipschitz continuity.In this paper, we…
We show that the existence of a non-coercive Lyapunov function is sufficient for uniform global asymptotic stability (UGAS) of infinite-dimensional systems with external disturbances provided the speed of decay is measured in terms of the…
We study integral-to-integral input-to-state stability for infinite-dimensional linear systems with inputs and trajectories in $L^p$-spaces. We start by developing the corresponding admissibility theory for linear systems with unbounded…
We consider time-delay systems with a finite number of delays in the state space $L^\infty\times\mathbb{R}^n$. In this framework, we show that forward completeness implies the bounded reachability sets property, while this implication was…
Given a nonlinear control system, a target set, a nonnegative integral cost, and a continuous function $W$, we say that the system is globally asymptotically controllable to the target with W-regulated cost, whenever, starting from any…
We propose a composite Lyapunov framework for nonlinear autonomous systems that ensures strict decay through a pair of differential inequalities. The approach yields integral estimates, quantitative convergence rates, vanishing of…
Time-invariant finite-dimensional systems, under reasonable continuity assumptions, exhibit the property that if solutions exist for all future times, the set of vectors reachable from a bounded set of initial conditions over bounded time…
We show that the robust forward completeness for distributed parameter systems is equivalent to the existence of a corresponding Lyapunov function that increases at most exponentially along the trajectories.
In this paper, a class of abstract dynamical systems is considered which encompasses a wide range of nonlinear finite- and infinite-dimensional systems. We show that the existence of a non-coercive Lyapunov function without any further…
We provide several characterizations of convergence to unstable equilibria in nonlinear systems. Our current contribution is three-fold. First we present simple algebraic conditions for establishing local convergence of non-trivial…
In this work, we give sufficient conditions for the almost global asymptotic stability of a cascade in which the subsystems are only almost globally asymptotically stable. The result is extended to upper triangular systems of arbitrary…
We prove a robust converse barrier function theorem via the converse Lyapunov theory. While the use of a Lyapunov function as a barrier function is straightforward, the existence of a converse Lyapunov function as a barrier function for a…
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…