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In this paper, we propose a new convex approach to stability analysis of nonlinear systems with polynomial vector fields. First, we consider an arbitrary convex polytope that contains the equilibrium in its interior. Then, we decompose the…
We analyze the exponential stability of distributed parameter systems. The system we consider is described by a coupled parabolic partial differential equation with spatially varying coefficients. We approximate the coefficients by…
A topological approach and understanding to the detection of unstable periodic orbits based on a recently proposed method (PRL 78, 4733 (1997)) is developed. This approach provides a classification of the set of transformations necessary…
This paper investigates a well-posedness property of parametric constraint systems named here Robinson stability. Based on advanced tools of variational analysis and generalized differentiation, we derive first-order and second-order…
In this paper, we first prove an abstract theorem on the existence of polynomial attractors and the concrete estimate of their attractive velocity for infinite-dimensional dynamical systems, then apply this theorem to a class of wave…
In this paper, we study the existence of higher order Poisson type systems. In detail, we prove a Residue type phenomenon for the fundamental solution of Laplacian in $\RR^n, n\ge 3$. This is analogous to the Residue theorem for the Cauchy…
Several results regarding the stability and the stabilization of linear impulsive positive systems under arbitrary, constant, minimum, maximum and range dwell-time are obtained. The proposed stability conditions characterize the pointwise…
In the present paper, we study observer design and we establish some sufficient conditions for practical exponential stability for a class of time-delay nonlinear systems written in triangular form. In case of delay, the exponential…
We present a method for synthesizing dynamic, reduced-order output-feedback polynomial control policies for control-affine nonlinear systems which guarantees runtime stability to a goal state, when using visual observations and a learned…
In this paper we are concerned with numerical methods for the one-sided event location in discontinuous differential problems, whose event function is nonlinear (in particular, of polynomial type). The original problem is transformed into…
This paper is concerned with stability analysis of nonlinear time-varying systems by using Lyapunov function based approach. The classical Lyapunov stability theorems are generalized in the sense that the time-derivative of the Lyapunov…
We investigate an example of noise-induced stabilization in the plane that was also considered in (Gawedzki, Herzog, Wehr 2010) and (Birrell, Herzog, Wehr 2011). We show that despite the deterministic system not being globally stable, the…
We consider initial-boundary-value problems for a class of nonlinear third order equations having non-autonomous forcing terms and get new asymptotic stability results by means of the Liapunov second method. The class includes equations…
We show that the probability distribution function that best fits the distribution of return times between two consecutive visits of a chaotic trajectory to finite size regions in phase space deviates from the exponential statistics by a…
The exponential ordering is exploited in the context of non-auto\-no\-mous delay systems, inducing monotone skew-product semiflows under less restrictive conditions than usual. Some dynamical concepts linked to the order, such as…
This study introduces a modified quadratic Lorenz attractor. The properties of this new chaotic system are analysed and discussed in detail, by determining the equilibria points, the eigenvalues of the Jacobian, and the Lyapunov exponents.…
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…
We prove the orbital stability of periodic traveling-wave solutions for systems of dispersive equations with coupled nonlinear terms. Our method is basically developed under two assumptions: one concerning the spectrum of the linearized…
Quadratic-bilinear (QB) systems arise in many areas of science and engineering. In this paper, we present a scalable approach for designing locally stabilizing state-feedback control laws and certifying the local stability of QB systems.…
We study the Lyapunov stability of stationary solutions to contact-type Hamilton-Jacobi equations on a compact manifold. Previous works typically assume $C^3$ Tonelli Hamiltonians and characterize stability in terms of Mather measures. In…