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Optimal quadratic Lyapunov functions for robust stability problem

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Dynamics and Control

Abstract

The robust stability problem for nominally linear system with nonlinear, time-varying structured perturbations is considered. The system is of the form

$$\dot x = A_N x + \sum\limits_{j = 1}^q { p_j A_j x.} $$

The Lyapunov direct method has been often utilized to determine the bounds for nonlinear, time-dependent functions pj, which can be tolerated by a stable nominal system. In most cases, quadratic forms are used either as components of vector Lyapunov function or as a function itself. The resulting estimates are usually conservative. Optimizing the Lyapunov function reduces the conservatism of the bounds. The main result of this article is the theorem which makes possible a recursive procedure of a design of optimal Lyapunov function. Examples demonstrate application of the proposed method.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Oregon State University, 91331, Corwallis, OR

    A. Glas

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  1. A. Glas
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Glas, A. Optimal quadratic Lyapunov functions for robust stability problem. Dynamics and Control 2, 265–279 (1992). https://doi.org/10.1007/BF02169517

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