Related papers: Quantization of Lyapunov functions
We explicitly construct global strict Lyapunov functions for rapidly time-varying nonlinear control systems. The Lyapunov functions we construct are expressed in terms of oftentimes more readily available Lyapunov functions for the limiting…
In this paper we present a technique for constructing Lyapunov functions based on Whitney's size functions. Applications to asymptotically stable equilibrium points, isolated sets, expansive homeomorphisms and continuum-wise expansive…
This paper proposes a method for certifying the local asymptotic stability of a given nonlinear Ordinary Differential Equation (ODE) by using Sum-of-Squares (SOS) programming to search for a partially quadratic Lyapunov Function (LF). The…
A class of asymptotically autonomous systems on the plane with oscillatory coefficients is considered. It is assumed that the limiting system is Hamiltonian with a stable equilibrium. The effect of damped multiplicative stochastic…
This paper presents new sufficient conditions for convergence and asymptotic or exponential stability of a stochastic discrete-time system, under which the constructed Lyapunov function always decreases in expectation along the system's…
In this note, we propose coordinate-invariant notions of incremental Lyapunov function and provide characterizations of incremental stability in terms of existence of the proposed Lyapunov functions.
Lyapunov stability of a mechanical system means that the dynamic response stays bounded in an arbitrarily small neighborhood of a static equilibrium configuration under small perturbations in positions and velocities. This type of stability…
We consider polynomial differential equations and make a number of contributions to the questions of (i) complexity of deciding stability, (ii) existence of polynomial Lyapunov functions, and (iii) existence of sum of squares (sos) Lyapunov…
In this paper, we investigate a class of hybrid stochastic heat equations. By explicit formulae of solutions, we not only reveal the sample Lyapunov exponents but also discuss the $p$th moment Lyapnov exponents. Moreover, several examples…
This paper studies deterministic and stochastic fixed-time stability of autonomous nonlinear discrete-time (DT) systems. Lyapunov conditions are first presented under which the fixed-time stability of deterministic DT system is certified.…
In this paper, we present an algorithm for stability analysis of systems described by coupled linear Partial Differential Equations (PDEs) with constant coefficients and mixed boundary conditions. Our approach uses positive matrices to…
The problem of formulating self-consistent local and global stability exponents is shown to require global separation of variables. Posing the separation of variable problem, we see that many such separations are possible, but only one is…
This paper studies finite-time stability and instability theorems in probability sense for stochastic nonlinear systems. Firstly, a new sufficient condition is proposed to guarantee that the considered system has a global solution.…
We study the stability properties of a class of time-varying nonlinear systems. We assume that non-strict input-to-state stable (ISS) Lyapunov functions for our systems are given and posit a mild persistency of excitation condition on our…
We study the concentration phenomenon for discrete-time random dynamical systems with an unbounded state space. We develop a heuristic approach towards obtaining exponential concentration inequalities for dynamical systems using an entirely…
In this paper, we study the stability problem of a stochastic, nonlinear, discrete-time system. We introduce a linear transfer operator-based Lyapunov measure as a new tool for stability verification of stochastic systems. Weaker…
We present a stability analysis of the standard nonautonomous systems type for a recently introduced generalized Lane-Emden equation which is shown to explain the presence of some of the structures observed in the atomic spatial…
A numerical method is developed leading to Lyapunov operators to approximate the solution of two-dimensional Boussinesq equation. It consists of an order reduction method and a finite difference discretization. It is proved to be uniquely…
We propose and analyze a new candidate Lyapunov function for relaxation towards general nonequilibrium steady states. The proposed functional is obtained from the large time asymptotics of time-symmetric fluctuations. For driven Markov jump…
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…