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Connecting nonlinear incremental Lyapunov stability with the linearizations Lyapunov stability
Proceedings of the 44th IEEE Conference on Decision and Control, 2006In this paper, we reveal new connections between the incremental Lyapunov properties of a nonlinear system and the Lyapunov properties of its linearizations. We focus on (incremental) asymptotic and exponential stability. In contrast with other works on the incremental Lyapunov properties of nonlinear systems, our approach is based on extended spaces ...
Fromion, Vincent, Scorletti, Gérard
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Robust stability via polyhedral Lyapunov functions
2009 American Control Conference, 2009In this paper we study the robustness analysis problem for linear continuous-time systems subject to parametric time-varying uncertainties making use of piecewise linear (polyhedral) Lyapunov functions. A given class of Lyapunov functions is said to be “universal” for the uncertain system under consideration if the search of a Lyapunov function that ...
Amato, F., Ambrosino, R., Ariola, M.
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Stability of Lyapunov exponents
Ergodic Theory and Dynamical Systems, 1991AbstractWe 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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SENSITIVITY ANALYSIS AND LYAPUNOV STABILITY
IFAC Proceedings Volumes, 1964This 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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Stability Radii and Lyapunov Exponents
1990In 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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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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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's Stability Criteria for Plasmas
Journal of Mathematical Physics, 1963The 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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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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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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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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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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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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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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