Journal ArticleDOI
Maximal Lyapunov Functions and Domains of Attraction for Autonomous Nonlinear Systems
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This article is published in IFAC Proceedings Volumes.The article was published on 1981-08-01. It has received 103 citations till now. The article focuses on the topics: Lyapunov function & Attraction.read more
Citations
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Journal ArticleDOI
On the estimation of asymptotic stability regions: State of the art and new proposals
TL;DR: In this article, the authors provide a comprehensive survey of the existing methods and their applications in engineering fields, and present several examples of application of the proposed technique for low-order (second and third) systems.
Journal ArticleDOI
Brief paper: Local stability analysis using simulations and sum-of-squares programming
TL;DR: A methodology utilizing information from simulations to generate Lyapunov function candidates satisfying necessary conditions for bilinear constraints is proposed and Qualified candidates are used to compute invariant subsets of the region-of-attraction and to initialize various bil inear search strategies for further optimization.
Journal ArticleDOI
An analysis and design method for linear systems under nested saturation
A. Bateman,Zongli Lin +1 more
TL;DR: This paper considers a linear system under nested saturation, and shows a condition derived in terms of a set of auxiliary feedback gains for determining if a given ellipsoid is contractively invariant to be equivalent to linear matrix inequalities in the actual and Auxiliary feedback gains.
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A Generalization of Zubov's Method to Perturbed Systems
TL;DR: A generalization of Zubov's theorem on representing the domain of attraction via the solution of a suitable partial differential equation is presented for the case of perturbed systems with a singular fixed point and maximal robust Lyapunov functions can be characterized as viscosity solutions.
Journal ArticleDOI
Rational Lyapunov functions for estimating and controlling the robust domain of attraction
TL;DR: The paper shows that the computation of the best lower bound of the LERDA for chosen degrees of the SOS polynomials, which requires the solution of a nonconvex optimization problem with bilinear matrix inequalities (BMIs), can be reformulated as a quasi-conveX optimization problem under some conditions.
References
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Journal ArticleDOI
A computational method for determining quadratic lyapunov functions for non-linear systems
Edward J. Davison,E. M. Kurak +1 more
TL;DR: In this paper, the problem of automatically constructing a quadratic Lyapunov function V = x'Ax for a high order non-linear system given by x@? = f(x), f(0) = 0, where f is a continuous function of x which guarantees uniqueness of solutions of the system is dealt with.
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On Liapounoff's Conditions of Stability
TL;DR: In this paper, the authors introduce a new and more strict type of stability, equiasymptotic stability, whose relations to the stability of Liapounoff are discussed (Theorem 7 and Example 4).
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Direct method for transient stability studies in power system analysis
TL;DR: In this paper, it is shown that the classical direct methods, which are based on energy considerations, can be derived and generalized by means of Lyapunov's second method.
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The status of stability theory for deterministic systems
TL;DR: This paper attempts to summarize and place in perspective some of the recent contributions to stability theory with major emphasis on work which relates closely to applications in control, circuit theory, and aerospace systems.
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Power System Transient Stability: Regions Using Popov's Method
TL;DR: In this article, the authors apply Kalman's procedure for the construction of Lur'e-type Lyapunov functions to a single-machine system with and without a velocity governor.