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Local Hypoellipticity by Lyapunov Function
Abstract and Applied Analysis, 2016 We treat the local hypoellipticity, in the first degree, for a class of abstract differential operators complexes; the ones are given by the following differential operators: Lj=∂/∂tj+(∂ϕ/∂tj)(t,A)A, j=1,2,…,n, where A:D(A)⊂H→H is a self-adjoint linear ...
E. R. Aragão-Costa
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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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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 ...
V. Lakshmikantham, S. Leela
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Measurement + Control, 2023 The existence of a Lyapunov function is known to ensure either local or global stability of a system’s equilibrium state. Inspired by the control-Lyapunov method, we here construct a Lyapunov candidate function by analyzing a pendulum system’s total ...
Martinius Knudsen +3 more
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Stability of the Vallis System
Современные информационные технологии и IT-образование, 2022 In this paper, a variational method is proposed for obtaining the necessary (and sufficient) stability conditions for perturbed solutions of the system of Vallis equations.
Vladimir Nefedov +2 more
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Stability of the Lorentz System
Современные информационные технологии и IT-образование, 2021 In this paper, a variational method is proposed for obtaining the necessary (and sufficient) stability conditions for perturbed solutions of the system of Lorentz equations.
Vasiliy Tikhomirov +3 more
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A Novel Method for Optimal Control of Piecewise Affine Systems Using Semi-Definite Programming [PDF]
International Journal of Industrial Electronics, Control and Optimization, 2020 : In this paper, a novel optimal control design method by discontinuous quadratic Lyapunov function and continuous quadratic Lyapunov function for 2-dimensional piecewise affine systems via semi-definite programming and LMI constraints is proposed.In ...
Majid Akbarian +2 more
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Lyapunov function for cosmological dynamical system
Demonstratio Mathematica, 2017 We prove the asymptotic global stability of the de Sitter solution in the Friedmann-Robertson-Walker conservative and dissipative cosmology. In the proof we construct a Lyapunov function in an exact form and establish its relationship with the first ...
Szydłowski Marek, Krawiec Adam
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Automatica, 2011 Abstract Lyapunov functions are a fundamental tool to investigate the stability properties of equilibrium points in linear or nonlinear systems. Unfortunately, even if the existence of Lyapunov functions for asymptotically stable equilibrium points is guaranteed by converse Lyapunov theorems, the actual computation of the analytic expression of the ...
Sassano M., Astolfi A.
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Feedback Stabilization and Lyapunov Functions [PDF]
SIAM Journal on Control and Optimization, 2000 The authors consider the problem of finding a feedback stabilizing law \(x \to k(x)\) associated with a control system \(x'(t) = f(x(t),u(t))\). Using the concept of positional strategies introduced in the framework of differential games by Krasovskii and Subbotin in 1988, assuming the existence of a Lyapunov Lipschitz function \(V\) defined on the ...
Francis H. Clarke +3 more
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