Related papers: Input-to-state stability of interconnected hybrid …
This work explores Lyapunov characterizations of the input-output-to-state stability (IOSS) property for nonlinear systems. The notion of IOSS is a natural generalization of the standard zero-detectability property used in the linear case.…
This paper studies finite-time stability of a class of hybrid systems. We present sufficient conditions in terms of multiple generalized Lyapunov functions for the origin of the hybrid system to be finite-time stable. More specifically, we…
This article proposes an approach to construct a Lyapunov function for a linear coupled impulsive system consisting of two time-invariant subsystems. In contrast to various variants of small-gain stability conditions for coupled systems,…
A notion of detectability for nonlinear systems is discussed. Within the framework of ``input to state stability'' (ISS), a dual notion of ``output to state stability'' (OSS), and a more complete detectability notion, ``input-output to…
Input-to-state stability (ISS) for systems described by partial differential equations has seen intensified research activity recently, and in particular the class of boundary control systems, for which truly infinite-dimensional effects…
Due to unbounded input operators in partial differential equations (PDEs) with boundary inputs, there has been a long-held intuition that input-to-state stability (ISS) properties and finite gains cannot be established with respect to…
We derive converse Lyapunov theorems for input-to-state stability (ISS) of linear infinite-dimensional analytic systems. We show that input-to-state stability of a linear system does not imply existence of a coercive quadratic ISS Lyapunov…
We prove that under a small-gain condition, an interconnection of two globally incrementally exponentially stable systems inherits this property on any compact connected forward invariant set. It is also demonstrated that 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…
This paper studies the input-to-state stability (ISS) properties based on the method of Lyapunov functionals for a class of semi-linear parabolic partial differential equations (PDEs) with respect to boundary disturbances. In order to avoid…
We propose a time-discounted integral variant of incremental input/output-to-state stability (i-iIOSS) together with an equivalent Lyapunov function characterization. Continuity of the i-iIOSS Lyapunov function is ensured if the system…
We offer a compositional data-driven scheme for synthesizing controllers that ensure global asymptotic stability (GAS) across large-scale interconnected networks, characterized by unknown mathematical models. In light of each network's…
This paper studies integral input-to-state stability (iISS) of nonlinear impulsive systems with time-delay in both the continuous dynamics and the impulses. Several iISS results are established by using the method of Lyapunov-Krasovskii…
This paper addresses the robust stability of a boundary controlled system coupling two partial differential equations (PDEs), namely beam and string equations, in the presence of boundary and in-domain disturbances under the framework of…
This paper shows that a necessary and sufficient condition for the small-signal stability of an inverter-integrated power system can be expressed in terms of semidefinite matrix inequalities determined only by the synchronous reactance of…
This paper introduces small-gain sufficient conditions for $2$-contraction of feedback interconnected systems, on the basis of individual gains of suitable subsystems arising from a modular decomposition of the second additive compound…
For bilinear infinite-dimensional dynamical systems, we show the equivalence between uniform global asymptotic stability and integral input-to-state stability. We provide two proofs of this fact. One applies to general systems over Banach…
We consider the problem of asymptotic convergence to invariant sets in interconnected nonlinear dynamic systems. Standard approaches often require that the invariant sets be uniformly attracting. e.g. stable in the Lyapunov sense. This,…
The present work provides two alternatives to formulate time-discounted incremental input/output-to-state stability (i-IOSS) as a suitable detectability notion for general nonlinear systems with non-additive disturbances. Both formulations…
We prove characterizations of input-to-state stability (ISS) for a large class of infinite-dimensional control systems, including some classes of evolution equations over Banach spaces, time-delay systems, ordinary differential equations…