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Kernel Machine to Estimate a Lyapunov Function and Region of Attraction (ROA) for Nonlinear Systems
IEEE Access, 2023 The Lyapunov theory establishes the fundamental details to determine the stability and the Lyapunov function associated with an equilibrium point of a nonlinear system.
Afroza Shirin +2 more
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Finite Time Stability of Stochastic Hybrid Systems
Abstract and Applied Analysis, 2014 This paper considers the finite time stability of stochastic hybrid systems, which has both Markovian switching and impulsive effect. First, the concept of finite time stability is extended to stochastic hybrid systems.
Ying Yang, Guopei Chen
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Robust Stability for Impulsive Systems With Polytope Uncertainties
IEEE Access, 2019 This paper is concerned with robust stability for impulsive systems with polytope uncertainties. At first, the stability for impulsive systems without uncertainties is addressed by employing a Lyapunov-like functional.
Hanyong Shao, Wenjing Wang
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Dynamical analysis of a new fractional-order predator–prey system with Holling type-III functional
Advances in Difference Equations, 2021 In this paper, we consider a new fractional-order predator–prey model with Holling type-III functional response and stage structure. Based on the Lyapunov stability theory and by constructing a suitable Lyapunov functional, we obtain some sufficient ...
Lihua Dai +3 more
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Journal of Applied Mathematics, 2014 We investigate the qualitative behavior of a perturbed causal differential equation that differs in initial position and initial time with respect to the unperturbed causal differential equations.
Coşkun Yakar, Mustafa Bayram Gücen
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Stationary Stability for Evolutionary Dynamics in Finite Populations
Entropy, 2016 We demonstrate a vast expansion of the theory of evolutionary stability to finite populations with mutation, connecting the theory of the stationary distribution of the Moran process with the Lyapunov theory of evolutionary stability.
Marc Harper, Dashiell Fryer
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A graph-theoretic approach to global input-to-state stability for coupled control systems
Advances in Difference Equations, 2017 In this paper, the input-to-state stability for coupled control systems is investigated. A systematic method of constructing a global Lyapunov function for the coupled control systems is provided by combining graph theory and the Lyapunov method ...
Yu Qiao, Yue Huang, Minghao Chen
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Adaptive Control Design for Arneodo Chaotic System with Uncertain Parameters and Input Saturation
Advances in Mathematical Physics, 2020 In this paper, tracking controller and synchronization controller of the Arneodo chaotic system with uncertain parameters and input saturation are considered. An adaptive tracking control law and an adaptive synchronization control law are proposed based
Chunhua Cheng +4 more
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A Tutorial on Incremental Stability Analysis using Contraction Theory [PDF]
Modeling, Identification and Control, 2010 This paper introduces a methodology for differential nonlinear stability analysis using contraction theory (Lohmiller and Slotine, 1998). The methodology includes four distinct steps: the descriptions of two systems to be compared (the plant and the ...
J. Jouffroy, T.I. Fossen
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Effective synchronization of a class of Chua's chaotic systems using an exponential feedback coupling [PDF]
, 2013 In this work a robust exponential function based controller is designed to synchronize effectively a given class of Chua's chaotic systems. The stability of the drive-response systems framework is proved through the Lyapunov stability theory.
Bowong, Samuel +4 more
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