相关论文: A Trek Rule for the Lyapunov Equation

This paper studies structured products of real matrices for which the top Lyapunov exponent can be accessed by reducing the dynamics to an amenable generalization of upper triangular matrices. Exploiting prescribed zero patterns (including…

This paper studies the use of vector Lyapunov functions for the design of globally stabilizing feedback laws for nonlinear systems. Recent results on vector Lyapunov functions are utilized. The main result of the paper shows that the…

This paper considers a wide class of smooth continuous dynamic nonlinear systems (control objects) with a measurable vector of state. The problem is to find a special function (Lyapunov function), which in the framework of the second…

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…

The feedback linearization method is further developed for the controller design on general nonlinear systems. Through the Lyapunov stability theory, the intractable nonlinear implicit algebraic control equations are effectively solved, and…

The Avalanche principle, in its original setting, together with large deviations yields a systematic way of proving the continuity of the Lyapunov exponent. In this text we present a geometric version of the Avalanche Principle in the…

This paper is concerned with stability analysis and synthesis for discrete-time linear systems with stochastic dynamics. Equivalence is first proved for three stability notions under some key assumptions on the randomness behind the…

In the study of chaotic behaviour of systems of many hard spheres, Lyapunov exponents of small absolute value exhibit interesting characteristics leading to speculations about connections to non-equilibrium statistical mechanics. Analytical…

Understanding and predicting how complex systems respond to external perturbations is a central challenge in nonequilibrium statistical physics. Here we consider continuous-time Markov networks, which we subject to perturbations along a…

The nonlinear Markov processes are the measure-valued dynamical systems which preserve positivity. They can be represented as the law of large numbers limits of general Markov models of interacting particles. In physics, the kinetic…

Contraction analysis is a stability theory for nonlinear systems where stability is defined incrementally between two arbitrary trajectories. It provides an alternative framework in which to study uncertain interconnections or systems with…

The fundamental matrix and the delay Lyapunov matrix of linear delay difference equations are introduced. Some properties of the Lyapunov matrix, and the jump discontinuities of its derivative are proven, leading to its construction in the…

The paper gives an overview of recent advances in structural equation modeling. A structural equation model is a multivariate statistical model that is determined by a mixed graph, also known as a path diagram. Our focus is on the…

Estimating the Region of Attraction (RoA) for nonlinear dynamical systems is a fundamental problem in control theory, with direct implications for stability analysis and safe controller design. Traditional approaches rely on analytically…

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…

The continuous-time differential Lyapunov equation is widely used in linear optimal control theory, a branch of mathematics and engineering. In quantum physics, it is known to appear in Markovian descriptions of linear (quadratic…

We analyse the so-called Marginal Instability of linear switching systems, both in continuous and discrete time. This is a phenomenon of unboundedness of trajectories when the Lyapunov exponent is zero. We disprove two recent conjectures of…

We consider a nonlinear stochastic differential equation driven by an $\alpha$-stable L\'{e}vy process ($1<\alpha<2$). We first obtain some regularity results for the probability density of its invariant measure via establishing the a…

Techniques from numerical bifurcation theory are very useful to study transitions between steady fluid flow patterns and the instabilities involved. Here, we provide computational methodology to use parameter continuation in determining…

Systems described by equations involving both multiplicative and additive noise are common in nature. Examples include convection of a passive scalar field, polymersin turbulent flow, and noise in dye lasers. In this paper the one component…