相关论文: Convergence Rate of Nonlinear Switched Systems

In this work, we present the equivalent of many theorems available for continuous time systems. In particular, the theory is applied to Averaging Theory and Separation of time scales. In particular the proofs developed for Averaging Theory…

In this paper, we aim to study the asymptotic behaviour for a class of McKean-Vlasov stochastic partial differential equations with slow and fast time-scales. Using the variational approach and classical Khasminskii time discretization, we…

We study the convergence speed of distributed iterative algorithms for the consensus and averaging problems, with emphasis on the latter. We first consider the case of a fixed communication topology. We show that a simple adaptation of a…

In this paper we prove a rate of convergence for the continuous time filtering solution of a multiple timescale correlated nonlinear system to a lower dimensional filtering equation in the limit of large timescale separation. Correlation is…

In this article, we provide a general strategy based on Lyapunov functionals to analyse global asymptotic stability of linear infinite-dimensional systems subject to nonlinear dampings under the assumption that the origin of the system is…

For a class of linear switched systems in continuous time a controllability condition implies that state feedbacks allow to achieve almost sure stabilization with arbitrary exponential decay rates. This is based on the Multiplicative…

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…

We present a set of results concerning the existence of Lyapunov-Krasovskii functionals for classes of nonlinear switched systems with time-delay. In particular, we first present a result for positive systems that relaxes conditions…

Consideration is given to the three different analytical methods for the computation of upper bounds for the rate of convergence to the limiting regime of one specific class of (in)homogeneous continuous-time Markov chains. This class is…

We first establish strong convergence rates for multiscale systems driven by $\alpha$-stable processes, with analyses constructed in two distinct scaling regimes. When addressing weak convergence rates of this system, we derive four…

For complex nonlinear systems, it is challenging to design algorithms that are fast, scalable, and give an accurate approximation of the stability region. This paper proposes a sampling-based approach to address these challenges. By…

While ensuring stability for linear systems is well understood, it remains a major challenge for nonlinear systems. A general approach in such cases is to compute a combination of a Lyapunov function and an associated control policy.…

Prediction-based transformation is applied to control-affine systems with distributed input delays. Transformed system state is calculated as a prediction of the system's future response to the past input with future input set to zero.…

In this study, we investigate the ISS of impulsive switched systems that have modes with both stable and unstable flows. We assume that the switching signal satisfies mode-dependent average dwell and leave time conditions. To establish ISS…

Let $(X_i)_{i=1,...,n}$ be a possibly nonstationary sequence such that $\mathscr{L}(X_i)=P_n$ if $i\leq n\theta$ and $\mathscr{L}(X_i)=Q_n$ if $i>n\theta$, where $0<\theta <1$ is the location of the change-point to be estimated. We…

We prove that for every discrete-time linear switching system in two complex variables and with finitely many switching states, either the system is Lyapunov stable or there exists a trajectory which escapes to infinity with at least linear…

We construct a marginally stable linear switching system in continuous time, in four dimensions and with three switching states, which is exponentially stable with respect to constant switching laws and which has a unique Barabanov norm,…

This paper answers the question if a qualitatively heterogeneous passive networked system containing damped and undamped nodes shows consensus in the output of the nodes in the long run. While a standard Lyapunov analysis shows that the…

This note investigates the stability of both linear and nonlinear switched systems with average dwell time. Two new analysis methods are proposed. Different from existing approaches, the proposed methods take into account the sequence in…

Some sufficient conditions on the algebraic stability of non-homogeneous regime-switching diffusion processes are established. In this work we focus on determining the decay rate of a stochastic system which switches randomly between…