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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…

Systems and Control · Computer Science 2019-03-01 Yohei Hosoe , Tomomichi Hagiwara

In this paper, we consider the stability of discrete-time linear switched systems with a common non-strict Lyapunov matrix.

Optimization and Control · Mathematics 2011-08-02 Xiongping Dai , Yu Huang , Mingqing Xiao

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

We provide explicit conditions for uniform stability, global asymptotic stability and uniform exponential stability for dynamic equations with a single delay and a nonnegative coefficient. Some examples on nonstandard time scales are also…

Dynamical Systems · Mathematics 2019-02-21 Elena Braverman , Basak Karpuz

Robust stabilization conditions for uncertain switched affine systems subject to a unitary input delay are presented. They are obtained through the Lyapunov framework and a min-switching state-feedback predictive control law. The result…

Systems and Control · Electrical Eng. & Systems 2026-04-20 Gerson Portilla , Carolina Albea , Alexandre Seuret

We present generalised Lyapunov-Razumikhin techniques for establishing global asymptotic stability of steady-state solutions of scalar delay differential equations. When global asymptotic stability cannot be established, the technique can…

Dynamical Systems · Mathematics 2021-12-03 F. M. G. Magpantay , A. R. Humphries

We investigate discret conditions for stability and asymptotic stability by Lyapunov and the point of equilibrium of autonomous system of differential equations.

Dynamical Systems · Mathematics 2010-07-02 Yulia Sharko

In this technical communique, we generalize the well-known Lyapunov-based stabilizability and detectability tests for discrete-time linear time-invariant systems to polytopic linear parameter-varying systems using the class of so-called…

Optimization and Control · Mathematics 2026-02-03 T. J. Meijer , V. S. Dolk , W. P. M. H. Heemels

We revisit the canonical continuous-time and discrete-time matrix algebraic and matrix differential equations that play a central role in Lyapunov based stability arguments. The goal is to generalize and extend these types of equations and…

Optimization and Control · Mathematics 2009-10-13 John M. Davis , Ian A. Gravagne , Robert J. Marks , Alice A. Ramos

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…

Optimization and Control · Mathematics 2013-11-20 A. Yu. Aleksandrov , Oliver Mason

A class of discrete-time nonlinear positive time-delay switched systems with sector-type nonlinearities is studied. Sufficient conditions for the existence of common and switched diagonal Lyapunov--Krasovskii functionals for this system…

Optimization and Control · Mathematics 2017-10-02 Alexander Aleksandrov , Oliver Mason

Three similar convergence notions are considered. Two of them are the long established notions of convergent dynamics and incremental stability. The other is the more recent notion of contraction analysis. All three convergence notions…

Optimization and Control · Mathematics 2018-11-06 Duc N. Tran , Björn S. Rüffer , Christopher M. Kellett

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…

Analysis of PDEs · Mathematics 2018-12-12 Lucie Baudouin , Alexandre Seuret , Frédéric Gouaisbaut

New sufficient conditions for the characterization of dwell-times for linear impulsive systems are proposed and shown to coincide with continuous decrease conditions of a certain class of looped-functionals, a recently introduced type of…

Optimization and Control · Mathematics 2012-06-05 Corentin Briat , Alexandre Seuret

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

A new functional-based approach is developed for the stability analysis of linear impulsive systems. The new method, which introduces looped-functionals, considers non-monotonic Lyapunov functions and leads to LMIs conditions devoid of…

Optimization and Control · Mathematics 2012-07-10 Corentin Briat , Alexandre Seuret

We analyze the stability properties of Lur'e systems with piecewise continuous nonlinearities by exploiting the notion of set-valued Lie derivative for Lur'e-Postnikov Lyapunov functions. We first extend an existing result of the literature…

Systems and Control · Electrical Eng. & Systems 2023-02-03 Simone Mariano , Romain Postoyan , Luca Zaccarian

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 work studies the problem of searching for homogeneous polynomial Lyapunov functions for stable switched linear systems. Specifically, we show an equivalence between polynomial Lyapunov functions for systems of this class and quadratic…

Systems and Control · Electrical Eng. & Systems 2020-02-20 Matthew Abate , Corbin Klett , Samuel Coogan , Eric Feron

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