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Lyapunov's theorem provides a fundamental characterization of the stability of dynamical systems. This paper presents a categorical framework for Lyapunov theory, generalizing stability analysis with Lyapunov functions categorically. Core…

Dynamical Systems · Mathematics 2025-08-01 Aaron D. Ames , Joe Moeller , Paulo Tabuada

This paper studies a class of random nonlinear systems with time-varying delay, in which the $r$-order moment ($r\geq1$) of the random disturbance is finite. Firstly, some general conditions are proposed to guarantee the existence and…

Optimization and Control · Mathematics 2018-06-22 Yao Liqiang , Zhang Weihai

This paper proposes a line integral Lyapunov function approach to stability analysis and stabilization for It\^o stochastic T-S models. Unlike the deterministic case, stability analysis of this model needs the information of Hessian matrix…

Systems and Control · Electrical Eng. & Systems 2020-04-02 Shaosheng Zhou , Yingying Han , Baoyong Zhang

This thesis addresses the question of stability of systems defined by differential equations which contain nonlinearity and delay. In particular, we analyze the stability of a well-known delayed nonlinear implementation of a certain…

Dynamical Systems · Mathematics 2007-05-23 Matthew M. Peet

In this paper, we present a new method for the dissipativity and stability analysis of a linear coupled differential-difference system (CDDS) with general distributed delays at both state and output. More precisely, the distributed delay…

Systems and Control · Computer Science 2018-11-06 Qian Feng , Sing Kiong Nguang , Alexandre Seuret

This note is concerned with stability analysis of integral delay systems with multiple delays. To study this problem, the well-known Jensen inequality is generalized to the case of multiple terms by introducing an individual slack weighting…

Dynamical Systems · Mathematics 2016-07-11 Bin Zhou , Zhao-Yan Li

We present a dual form of Lyapunov-Krasovskii functional which allows the problem of controller synthesis of multi-delay systems to be formulated and solved in a convex manner. First, we give a general form of dual stability condition…

Dynamical Systems · Mathematics 2016-05-16 Matthew M. Peet

An alternative approach for minimum and mode-dependent dwell-time characterization for switched systems is derived. The proposed technique is related to Lyapunov looped-functionals, a new type of functionals leading to stability conditions…

Optimization and Control · Mathematics 2012-09-05 Corentin Briat , Alexandre Seuret

This paper investigates the robustness of exponential stability of a class of switched systems described by linear functional differential equations under arbitrary switching. We will measure the stability robustness of such a system,…

Dynamical Systems · Mathematics 2022-03-08 Nguyen Khoa Son , Le Van Ngoc

New necessary and sufficient conditions are proposed for the stability investigation of dynamical systems using the flow and the divergence of the phase vector velocity. The obtained conditions generalize the well-known results of V.P.…

Optimization and Control · Mathematics 2019-05-17 Igor Furtat

This paper deals with the stability analysis problem of discrete-time switched linear systems with ranged dwell time. A novel concept called L-switching-cycle is proposed, which contains sequences of multiple activation cycles satisfying…

Optimization and Control · Mathematics 2021-06-01 Weiming Xiang

Consider the planar linear switched system $\dot x(t)=u(t)Ax(t)+(1-u(t))Bx(t),$ where $A$ and $B$ are two $2\times2$ real matrices, $x \in \R^2$, and $u(.):[0,\infty[\to\{0,1\}$ is a measurable function. In this paper we consider the…

Optimization and Control · Mathematics 2007-05-23 Moussa Balde , Ugo Boscain

We address the stability problem for linear switching systems with mode-dependent restrictions on the switching intervals. Their lengths can be bounded as from below (the guaranteed dwell-time) as from above. The upper bounds make this…

Optimization and Control · Mathematics 2022-06-01 Vladimir Yu. Protasov , Rinat Kamalov

We study stability criteria for discrete-time switched systems and provide a meta-theorem that characterizes all Lyapunov theorems of a certain canonical type. For this purpose, we investigate the structure of sets of LMIs that provide a…

Optimization and Control · Mathematics 2018-01-24 Raphael M. Jungers , Amirali Ahmadi , Pablo Parrilo , Mardavij Roozbehani

In this paper, we present sufficient conditions for asymptotic stability and exponential stability of a class of impulsive neutral differential equations with discrete and distributed delays. Our approaches are based on the method using…

Dynamical Systems · Mathematics 2025-04-03 Jinyuan Pan , Guiling Chen

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…

Systems and Control · Computer Science 2019-06-05 Yuzhen Qin , Ming Cao , Brian D. O. Anderson

The solvability of a delay differential equation arising in the construction of quadratic cost functionals, i.e. Lyapunov functionals, for a linear time-delay system with a constant and a distributed delay is investigated. We present a…

Systems and Control · Computer Science 2019-09-23 Suat Gumussoy , Murad Abu-Khalaf

This paper considers the stability problem of a linear time invariant system in feedback with a string equation. A new Lyapunov functional candidate is proposed based on the use of augmented states which enriches and encompasses the…

Analysis of PDEs · Mathematics 2019-04-25 Matthieu Barreau , Alexandre Seuret , Frédéric Gouaisbaut , Lucie Baudouin

Stability analysis and control of linear impulsive systems is addressed in a hybrid framework, through the use of continuous-time time-varying discontinuous Lyapunov functions. Necessary and sufficient conditions for stability of impulsive…

Optimization and Control · Mathematics 2013-11-15 Corentin Briat

This article proposes an approach to construct a Lyapunov function for a linear coupled impulsive system consisting of two time-invariant subsystems. In contrast to various variants of small-gain stability conditions for coupled systems,…

Dynamical Systems · Mathematics 2023-08-11 Vitalii Slynko , Sergey Dashkovskiy , Ivan Atamas