Related papers: Relaxed ISS Small-Gain Theorems for Discrete-Time …
We consider a general class of nonlinear, constrained, discrete-time systems whose dynamics are parametrized by a set of gains. We define the semiglobal, practical, asymptotic stability (SPAS) of compact sets for this class of systems, and…
We present a new sufficient condition for finite-gain $L_2$ input-to-output stability of a networked system. The condition requires a matrix, that combines information on the $L_2$ gains of the sub-systems and their interconnections, to be…
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…
Small-gain conditions used in analysis of feedback interconnections are contraction conditions which imply certain stability properties. Such conditions are applied to a finite or infinite interval. In this paper we consider the case, when…
This paper demonstrates input-to-state stability (ISS) of the SIR model of infectious diseases with respect to the disease-free equilibrium and the endemic equilibrium. Lyapunov functions are constructed to verify that both equilibria are…
For general time-varying or switched (nonlinear) systems, converse Lyapunov theorems for stability are not available. In these cases, the integral input-to-state stability (iISS) property is not equivalent to the existence of an…
This paper considers the problem of finite-time stability for stochastic nonlinear systems. A new Lyapunov theorem of stochastic finite-time stability is proposed, and an important corollary is obtained. Some comparisons with the existing…
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…
The concept of input-to-state stability (ISS) proposed in the late 1980s is one of the central notions in robust nonlinear control. ISS has become indispensable for various branches of nonlinear systems theory, such as robust stabilization…
Incremental input-to-state stability (delta-ISS) offers a robust framework to ensure that small input variations result in proportionally minor deviations in the state of a nonlinear system. This property is essential in practical…
Input-to-State Stability (ISS) is fundamental in mathematically quantifying how stability degrades in the presence of bounded disturbances. If a system is ISS, its trajectories will remain bounded, and will converge to a neighborhood of an…
In this paper, we develop a new approach to study gain operators built from the interconnection gains of infinite networks of dynamical systems. Our focus is on the construction of paths of strict decay which are used for building Lyapunov…
This paper addresses characterizations of integral input-to-state stability (iISS) for hybrid systems. In particular, we give a Lyapunov characterization of iISS unifying and generalizing the existing theory for pure continuous-time and…
In this paper, we extend the notion of finite-time input-to-state stability (FTISS) for finite-dimensional systems to infinite-dimensional systems. More specifically, we first prove an FTISS Lyapunov theorem for a class of…
New trajectory-based small-gain results are obtained for nonlinear feedback systems under relaxed assumptions. Specifically, during a transient period, the solutions of the feedback system may not satisfy some key inequalities that previous…
We show that the existence of a Lyapunov-Krasovskii functional (LKF) with pointwise dissipation (i.e. dissipation in terms of the current solution norm) suffices for input-to-state stability, provided that uniform global stability can also…
We develop a model-free framework for stabilizing quantum states using only empirical finite-difference evaluations of a measurement-derived Lyapunov observable. The controller requires no knowledge of the Hamiltonian, dissipative…
This paper develops a neural network based control framework that ensures system safety and input-to-state stability (ISS) for general nonlinear switched systems with unknown dynamics. Leveraging the concept of dwell time, we derive…
A small-gain approach is proposed to analyze closed-loop stability of linear diffusion-reaction systems under finite-dimensional observer-based state feedback control. For this, the decomposition of the infinite-dimensional system into a…
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…