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This paper investigates the robust stabilisation of a class of fractional-order non-linear systems via fixed-order dynamic output feedback controller in terms of linear matrix inequalities (LMIs). The systematic stabilisation algorithm…

Optimization and Control · Mathematics 2019-06-05 Elyar Zavary , Mahdi Sojoodi

Lyapunov-like characterizations for non-uniform in time and uniform robust global asymptotic stability of uncertain systems described by retarded functional differential equations are provided.

Optimization and Control · Mathematics 2007-05-23 Iasson Karafyllis

A Lyapunov design method is used to analyze the nonlinear stability of a generic reservoir computer for both the cases of continuous-time and discrete-time dynamics. Using this method, for a given nonlinear reservoir computer, a radial…

Systems and Control · Electrical Eng. & Systems 2020-01-08 Afroza Shirin , Isaac S. Klickstein , Francesco Sorrentino

The paper describes a novel method for studying the stability of nonautonomous dynamical systems. This method based on the flow and divergence of the vector field with coupling to the method of Lyapunov functions. The necessary and…

Systems and Control · Electrical Eng. & Systems 2020-03-31 Igor Furtat

The stability analysis of a class of discontinuous discrete-time systems is studied in this paper. The system under study is modeled as a feedback interconnection of a linear system and a set-valued nonlinearity. An equivalent…

Systems and Control · Electrical Eng. & Systems 2022-08-12 Francesco Ferrante , Giorgio Valmorbida

We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that exponential stability implies the existence of a positive Lyapunov function which is quadratic on…

Dynamical Systems · Mathematics 2007-07-03 Matthew M. Peet , Antonis Papachristodoulou , Sanjay Lall

We show that the existence of a non-coercive Lyapunov function is sufficient for uniform global asymptotic stability (UGAS) of infinite-dimensional systems with external disturbances provided the speed of decay is measured in terms of the…

Dynamical Systems · Mathematics 2017-02-22 Andrii Mironchenko , Fabian R. Wirth

The Lyapunov inequality is an indispensable tool for stability analysis in linear control theory. It provides a necessary and sufficient condition for the stability of an autonomous linear-time invariant system in terms of the existence of…

Optimization and Control · Mathematics 2025-12-24 Avinash Kumar

We address the classic problem of stability and asymptotic stability in the sense of Lyapunov of the equilibrium point of autonomic differential equations using discrete approach. This new approach includes a consideration of a family of…

Classical Analysis and ODEs · Mathematics 2012-11-07 Eugene Polulyakh , Vladimir Sharko , Igor Vlasenko

Lyapunov functions provide a tool to analyze the stability of nonlinear systems without extensively solving the dynamics. Recent advances in sum-of-squares methods have enabled the algorithmic computation of Lyapunov functions for…

Dynamical Systems · Mathematics 2016-09-26 Soumya Kundu , Marian Anghel

This paper develops a new approach to the estimation of the degree of boundedness or stability of multidimensional nonlinear systems with time-dependent nonperiodic coefficients-an essential task in various engineering and natural science…

Dynamical Systems · Mathematics 2022-06-16 Mark A. Pinsky

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.…

Optimization and Control · Mathematics 2022-07-26 Weihai Zhang , Liqiang Yao

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.…

Machine Learning · Computer Science 2023-12-27 Junlin Wu , Andrew Clark , Yiannis Kantaros , Yevgeniy Vorobeychik

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

The present paper is mainly aimed at introducing a novel notion of stability of nonlinear time-delay systems called Rational Stability. According to the Lyapunov-type, various sufficient conditions for rational stability are reached. Under…

Optimization and Control · Mathematics 2018-09-17 Nadhem Echi , Boulbaba Ghanmi

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…

Dynamical Systems · Mathematics 2017-02-20 Umesh Vaidya

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 considers a sampling-based approach to stability verification for piecewise continuous nonlinear systems via Lyapunov functions. Depending on the system dynamics, the candidate Lyapunov function and the set of initial states of…

Systems and Control · Computer Science 2016-09-02 Ruxandra Bobiti , Mircea Lazar

This work studies stability and robustness of a nonlinear system given as an interconnection of an ODE and a parabolic PDE subjected to external disturbances entering through the boundary conditions of the parabolic equation. To this end we…

Analysis of PDEs · Mathematics 2022-11-07 S. Dashkovskiy , O. Kapustyan , V. Slynko

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