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Convergent, contractive or incremental stability properties of nonlinear systems have attracted interest for control tasks such as observer design, output regulation and synchronization. The convergence property plays a central role in the…
We consider interconnected nonlinear systems with external inputs, where each of the subsystems is assumed to be input-to-state stable (ISS). Sufficient conditions of small gain type are provided guaranteeing that the interconnection is ISS…
In a pedagogical but exhaustive manner, this survey reviews the main results on input-to-state stability (ISS) for infinite-dimensional systems. This property allows estimating the impact of inputs and initial conditions on both the…
A sufficient condition for the stability of a system resulting from the interconnection of dynamical systems is given by the small gain theorem. Roughly speaking, to apply this theorem, it is required that the gains composition is…
The notions of asymptotic amplitude for signals, and Cauchy gain for input/output systems, and an associated small-gain principle, are introduced. These concepts allow the consideration of systems with multiple, and possibly…
We prove the following converse of the passivity theorem. Consider a causal system given by a sum of a linear time-invariant and a passive linear time-varying input-output map. Then, in order to guarantee stability (in the sense of finite…
This paper provides sufficient conditions for global asymptotic stability and global exponential stability, which can be applied to nonlinear, large-scale, uncertain discrete-time systems. The conditions are derived by means of vector…
This paper develops a direct data-driven framework for infinite networks with unknown nonlinear polynomial subsystems, enabling the synthesis of controllers that ensure the entire network is uniformly globally asymptotically stable (UGAS).…
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…
From the structural perspective, this paper investigates a new formulation of the concept of input-to-state stability (ISS), and based on this formulation, proposes a new stability analysis approach for a class of interconnected system. The…
Motivated by an open problem posed by J.P. Hespanha, we extend the notion of Barabanov norm and extremal trajectory to classes of switching signals that are not closed under concatenation. We use these tools to prove that the finiteness of…
Despite modular conditions to guarantee stability for large-scale systems have been widely studied, few methods are available to tackle the case of networks with multiple equilibria. This paper introduces small-gain like sufficient…
In the present paper, a novel result for inferring uniform global, not semi-global, exponential stability in the sense of Lyapunov with respect to input-affine systems from global uniform exponential stability properties with respect to…
Given two nonlinear systems which only violate incremental passivity when their incremental gains are sufficiently small, we give a condition for their negative feedback interconnection to have finite incremental gain, which generalizes the…
This SSFG Lp stability theorem can predict permissible forcing amplitudes below which a finite nonlinear input-output gain can be maintained. Our analysis employs Linear Matrix Inequalities (LMI) and Sum-of-Squares (SOS) as the primary…
This paper provides necessary conditions and sufficient conditions for the (global) Input-to-State Stability property of simple uncertain vehicular-traffic network models under the effect of a PI-regulator. Local stability properties for…
We introduce the notions of semi-uniform input-to-state stability and its subclass, polynomial input-to-state stability, for infinite-dimensional systems. We establish a characterization of semi-uniform input-to-state stability based on…
In this paper we consider input-to-state stability (ISS) of impulsive control systems with and without time-delays. We prove that if the time-delay system possesses an exponential Lyapunov-Razumikhin function or an exponential…
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…
This paper studies the graph-theoretic conditions for stability of positive monotone systems. Using concepts from input-to-state stability and network small-gain theory, we first establish necessary and sufficient conditions for the…