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Journal of Applied Mathematics and Mechanics, 2006
The stability of the stationary point of a Lyapunov system [Malkin IG, Some Problems in the Theory of Non-linear Oscillations. Moscow: Gostekhizd; 1956.], which describes the perturbed motion of a dynamical system with two degrees of freedom, is investigated.
A.L. Kunitsyn, V.N. Tkhai
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The stability of the stationary point of a Lyapunov system [Malkin IG, Some Problems in the Theory of Non-linear Oscillations. Moscow: Gostekhizd; 1956.], which describes the perturbed motion of a dynamical system with two degrees of freedom, is investigated.
A.L. Kunitsyn, V.N. Tkhai
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1995
The second or direct method of Lyapunov is entirely different from pole analysis in philosophy, nature, and detail, although there are a few overlaps for linear time-invariant systems.
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The second or direct method of Lyapunov is entirely different from pole analysis in philosophy, nature, and detail, although there are a few overlaps for linear time-invariant systems.
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Stability: Lyapunov, Linear Systems
2014The notion of stability allows to study the qualitative behavior of dynamical systems. In particular it allows to study the behavior of trajectories close to an equilibrium point or to a motion. The notion of stability that we discuss has been introduced in 1882 by the Russian mathematician A.M.
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2017
In the preceding section we introduced a classification of cellular automata based on attractors, their number and structure. In the present section we focus on the complexity of the dynamics. The two aspects are not independent, but differ slightly. We start with Devaney’s definition of chaos, and relate this definition to the Hurley classification ...
Karl-Peter Hadeler, Johannes Müller
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In the preceding section we introduced a classification of cellular automata based on attractors, their number and structure. In the present section we focus on the complexity of the dynamics. The two aspects are not independent, but differ slightly. We start with Devaney’s definition of chaos, and relate this definition to the Hurley classification ...
Karl-Peter Hadeler, Johannes Müller
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Lyapunov Stability and Orbital Stability of Dynamical Systems
Differential Equations, 2004The paper deals with the study of the relationship between Lyapunov stability of motions and orbital stability of invariant sets. The author focuses the attention on the analysis of the qualitative behavior of trajectories in a neighborhood of an orbitally asymptotically stable set whose domain of attraction consists of Lyapunov stable motions.
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Sufficient lyapunov-like conditions for stabilization
Mathematics of Control, Signals, and Systems, 1989zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Lyapunov’s definition of stability
1969Let $$G\left[ u \right] = 0$$ (A) be an equation of motion which governs the motion of a given system completely (differential equation with proper boundary conditions, Hamilton’s principle in its general form, etc.; cf. sect. 9). In general u will be an N-dimensional vector, cf.
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Lyapunov-Based Stability Analysis
2014This chapter presents generalizations of the direct Lyapunov method to TDSs. In the first section, for general TDSs, the stability notions are defined, and Lyapunov–Krasovskii and Lyapunov–Razumikhin stability theorems are stated. The second section gives a short introduction to linear matrix inequalities. Sections 3.3–3.7 and 3.10 are devoted to delay-
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A Fuzzy Lyapunov Function Method to Stability Analysis of Fractional-Order T–S Fuzzy Systems
IEEE Transactions on Fuzzy Systems, 2022Zhanshan Wang
exaly