Topic
Control-Lyapunov function
About: Control-Lyapunov function is a research topic. Over the lifetime, 2596 publications have been published within this topic receiving 76215 citations.
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TL;DR: In this article, the authors present the first algorithms that allow the estimation of non-negative Lyapunov exponents from an experimental time series, which provide a qualitative and quantitative characterization of dynamical behavior.
8,128 citations
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TL;DR: It is shown that the regularity properties of the Lyapunov function and those of the settling-time function are related and converse Lyap Unov results can only assure the existence of continuous Lyap unov functions.
Abstract: Finite-time stability is defined for equilibria of continuous but non-Lipschitzian autonomous systems. Continuity, Lipschitz continuity, and Holder continuity of the settling-time function are studied and illustrated with several examples. Lyapunov and converse Lyapunov results involving scalar differential inequalities are given for finite-time stability. It is shown that the regularity properties of the Lyapunov function and those of the settling-time function are related. Consequently, converse Lyapunov results can only assure the existence of continuous Lyapunov functions. Finally, the sensitivity of finite-time-stable systems to perturbations is investigated.
3,894 citations
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TL;DR: In this paper, a general theory of dissipative dynamical systems is presented, where dissipativeness is defined in terms of an inequality involving the storage function and the supply function, which is bounded from below by the available storage and from above by the required supply.
Abstract: The first part of this two-part paper presents a general theory of dissipative dynamical systems. The mathematical model used is a state space model and dissipativeness is defined in terms of an inequality involving the storage function and the supply function. It is shown that the storage function satisfies an a priori inequality: it is bounded from below by the available storage and from above by the required supply. The available storage is the amount of internal storage which may be recovered from the system and the required supply is the amount of supply which has to be delivered to the system in order to transfer it from the state of minimum storage to a given state. These functions are themselves possible storage functions, i.e., they satisfy the dissipation inequality. Moreover, since the class of possible storage functions forms a convex set, there is thus a continuum of possible storage functions ranging from its lower bound, the available storage, to its upper bound, the required supply. The paper then considers interconnected systems. It is shown that dissipative systems which are interconnected via a neutral interconnection constraint define a new dissipative dynamical system and that the sum of the storage functions of the individual subsystems is a storage function for the interconnected system. The stability of dissipative systems is then investigated and it is shown that a point in the state space where the storage function attains a local minimum defines a stable equilibrium and that the storage function is a Lyapunov function for this equilibrium. These results are then applied to several examples. These concepts and results will be applied to linear dynamical systems with quadratic supply rates in the second part of this paper.
3,124 citations
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01 Sep 1983TL;DR: It remains an open question whether the Lyapunov function approach, which requires a study of equilibrium points, or an alternative global approach, such as the LyAPunov functional approach, will ultimately handle all of the physically important cases.
Abstract: Systems that are competitive and possess symmetric interactions admit a global Lyapunov function. However, a global Lyapunov function whose equilibrium set can be effectively analyzed has not yet been discovered. It remains an open question whether the Lyapunov function approach, which requires a study of equilibrium points, or an alternative global approach, such as the Lyapunov functional approach, which sidesteps a direct study of equilibrium points will ultimately handle all of the physically important cases.
2,440 citations
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TL;DR: This paper presents control designs for single-input single-output (SISO) nonlinear systems in strict feedback form with an output constraint, and explores the use of an Asymmetric Barrier Lyapunov Function as a generalized approach that relaxes the requirements on the initial conditions.
1,999 citations