Related papers: Lyapunov criteria for robust forward completeness …
This paper presents a counterexample-guided iterative algorithm to compute convex, piecewise linear (polyhedral) Lyapunov functions for uncertain continuous-time linear hybrid systems. Polyhedral Lyapunov functions provide an alternative to…
A random phase property establishing a link between quasi-one-dimensional random Schroedinger operators and full random matrix theory is advocated. Briefly summarized it states that the random transfer matrices placed into a normal system…
This paper presents a proof that existence of a polynomial Lyapunov function is necessary and sufficient for exponential stability of sufficiently smooth nonlinear ordinary differential equations on bounded sets. The main result states that…
In this paper we use a path-integral approach to represent the Lyapunov exponents of both deterministic and stochastic dynamical systems. In both cases the relevant correlation functions are obtained from a (one-dimensional) supersymmetric…
This paper studies robust output tracking and disturbance rejection for boundary controlled infinite-dimensional port--Hamiltonian systems including second order models such as the Euler--Bernoulli beam. The control design is achieved using…
We consider the problem of robust diffusive stability (RDS) for a pair of coupled stable discrete-time positive linear-time invariant (LTI) systems. We first show that the existence of a common diagonal Lyapunov function is sufficient for…
In this paper, by using a characterization of functions having fractional derivative, we propose a rigorous fractional Lyapunov function candidate method to analyze stability of fractional-order nonlinear systems. First, we prove an…
This paper is concerned with relationships of Lyapunov exponents with sensitivity and stability for non-autonomous discrete systems. Some new concepts are introduced for non-autonomous discrete systems, including Lyapunov exponents, strong…
In this work we addressed the problem of stability analysis for an uncertain piecewise affine model of a genetic regulatory network. In particular we considered polytopic parameter uncertainties on the proteins production rate functions,…
In recent years, statistical characterization of the discrete conservative dynamical systems (more precisely, paradigmatic examples of area-preserving maps such as the standard and the web maps) has been analyzed extensively and shown that,…
For a smooth expanding circle map, we show that the empirical distribution of Lyapunov exponents of periodic points of any fixed period is close to normal, with an error that decreases as the period grows. This establishes a version of the…
Consider a reflected jump-diffusion on the positive half-line. Assume it is stochastically ordered. We apply the theory of Lyapunov functions and find explicit estimates for the rate of exponential convergence to the stationary…
We consider linear iterated function systems with a random multiplicative error on the real line. Our system is $\{x\mapsto d_i + \lambda_i Y x\}_{i=1}^m$, where $d_i\in \R$ and $\lambda_i>0$ are fixed and $Y> 0$ is a random variable with…
We show, using generic globally-coupled systems, that the collective dynamics of large chaotic systems is encoded in their Lyapunov spectra: most modes are typically localized on a few degrees of freedom, but some are delocalized, acting…
We provide a distributed coordinated approach to the stability analysis and control design of large-scale nonlinear dynamical systems by using a vector Lyapunov functions approach. In this formulation the large-scale system is decomposed…
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…
As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov…
Fixed-time stable dynamical systems are capable of achieving exact convergence to an equilibrium point within a fixed time that is independent of the initial conditions of the system. This property makes them highly appealing for designing…
We give a succinct and self-contained description of the synchronized motion on networks of mutually coupled oscillators. Usually, the stability criterion for the stability of synchronized motion is obtained in terms of Lyapunov exponents.…
We develop a practical approach to establish the stability, that is, the recurrence in a given set, of a large class of controlled Markov chains. These processes arise in various areas of applied science and encompass important numerical…