Results 181 to 190 of about 14,438 (228)

Stability Radii and Lyapunov Exponents

1990
In the state space approach to stability of uncertain systems the concept of stability radius plays a central role. In this paper we use the classical concept of Lyapunov exponents, which describe the exponential growth behavior, in order to define a variety of stability and instability radii for families of linear systems ẋ = [A + u(t)]x, u(t) ∈ U ρ ,
Colonius, Fritz, Kliemann, Wolfgang
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SENSITIVITY ANALYSIS AND LYAPUNOV STABILITY

IFAC Proceedings Volumes, 1964
This chapter focuses on sensitivity analysis and Lyapunov stability. Sensitivity analysis is an extension and development of a rather old idea, which became known in the theory of partial differential equations under the name of a correctly set problem.
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Lyapunov's Stability Criteria for Plasmas

Journal of Mathematical Physics, 1963
The orbit stability theory of Lyapunov has been adapted to the Vlasov-Boltzmann equation governing plasmas. Both linear and nonlinear stability are considered. The theory is characterized by a search for Lyapunov functions, whose existence implies stability in analogy with particles trapped in a potential well, as in the energy principle.
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Lyapunov Stability and Orbital Stability of Dynamical Systems

Differential Equations, 2004
The 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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Stability of Lyapunov exponents

Ergodic Theory and Dynamical Systems, 1991
AbstractWe consider small random perturbations of matrix cocycles over Lipschitz homeomorphisms of compact metric spaces. Lyapunov exponents are shown to be stable provided that our perturbations satisfy certain regularity conditions. These results are applicable to dynamical systems, particularly to volume-preserving diffeomorphisms.
Ledrappier, F., Young, L.-S.
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Sufficient lyapunov-like conditions for stabilization

Mathematics of Control, Signals, and Systems, 1989
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Lyapunov Stability of Motion

2012
The main intent of this chapter is to introduce the essential mathematical tools for stability analysis of continuous finite-dimensional dynamical systems. We begin with an overview of sufficient conditions to guarantee existence and uniqueness of the system solutions, followed by a collection of Lyapunov-based methods for studying stability of the ...
Eugene Lavretsky, Kevin A. Wise
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Lyapunov Stability Theory

1999
The study of the stability of dynamical systems has a very rich history. Many famous mathematicians, physicists, and astronomers worked on axiomatizing the concepts of stability. A problem, which attracted a great deal of early interest was the problem of stability of the solar system, generalized under the title “the N-body stability problem.” One of ...
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Lyapunov Stability Theory

2018
Stability of nonlinear systems are discussed in this chapter. Lyapunov stability, asymptotic stability, and exponential stability of an equilibrium point of a nonlinear system are defined. The Lyapunov’s direct method is introduced as an indispensable tool for analyzing stability of nonlinear systems.
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Lyapunov Stability Theory

2014
Basic concepts for the Lyapunov stability are introduced. Conditions are obtained for the stability of linear equations with constant, periodic, and general variable coefficients. Linearization and Lyapunov functions are used to deal with nonlinear stability problems.
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