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A Discussion on the Existence of Smooth Lyapunov Functions for Continuous Stable Systems [PDF]
International Journal of Industrial Electronics, Control and Optimization, 2021 Lyapunov's theorem is the basic criteria to establish the stability properties of the nonlinear dynamical systems. In this method, it is a necessity to find the positive definite functions with negative definite or negative semi-definite derivative ...
Majid Akbarian, Naser Pariz
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The Investigation of Nonlinear Polynomial Control Systems
Моделирование и анализ информационных систем, 2021 The paper considers methods for estimating stability using Lyapunov functions, which are used for nonlinear polynomial control systems. The apparatus of the Gro¨bner basis method is used to assess the stability of a dynamical system. A description of the
Sergei Nikolaevich Chukanov +1 more
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Mathematics, 2023 In recent years, various qualitative investigations of the properties of differential equations with different types of generalizations of Riemann–Liouville fractional derivatives were studied and stability properties were investigated, usually using ...
Ravi P. Agarwal +2 more
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A General Multipatch Model of Ebola Dynamics
Nonautonomous Dynamical Systems, 2021 A model for the transmission dynamics of Ebola virus in a multipatch network setting is studied. The model considers the contribution to the dynamics by people who are susceptible, infectious, isolated, deceased but still infectious and not yet buried ...
Rebaza Jorge
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Eigenpairs for the Analysis of Complete Lyapunov Functions
Complexity, 2022 A complete Lyapunov function describes the qualitative behaviour of a dynamical system: the areas where the orbital derivative vanishes and where it is strictly negative characterise the chain recurrent set and the gradient-like flow, respectively ...
Carlos Argáez +2 more
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On perturbing lyapunov functions [PDF]
Mathematical Systems Theory, 1976 A new idea of perturbing Lyapunov functions is presented which permits one to discuss nonuniform properties of solutions of differential equations under weaker ...
Lakshmikantham, V., Leela, S.
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Finite-Time Lyapunov Functions and Impulsive Control Design
Complexity, 2020 In this paper, we introduce finite-time Lyapunov functions for impulsive systems. The relaxed sufficient conditions for asymptotic stability of an equilibrium of an impulsive system are given via finite-time Lyapunov functions.
Huijuan Li, Qingxia Ma
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Constructions of Strict Lyapunov Functions for Discrete Time and Hybrid Time-Varying Systems [PDF]
, 2006 We provide explicit closed form expressions for strict Lyapunov functions for time-varying discrete time systems. Our Lyapunov functions are expressed in terms of known nonstrict Lyapunov functions for the dynamics and finite sums of persistency of ...
Albertini +24 more
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Further Remarks on Strict Input-to-State Stable Lyapunov Functions for Time-Varying Systems [PDF]
, 2004 We study the stability properties of a class of time-varying nonlinear systems. We assume that non-strict input-to-state stable (ISS) Lyapunov functions for our systems are given and posit a mild persistency of excitation condition on our given Lyapunov ...
Angeli +20 more
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An Inverse Dynamics Approach to Control Lyapunov Functions [PDF]
, 2020 With the goal of moving towards implementation of increasingly dynamic behaviors on underactuated systems, this paper presents an optimization-based approach for solving full-body dynamics based controllers on underactuated bipedal robots.
abe, betts, murray, sastry, sentis
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