Robust-Control By 2 Lyapunov Functions

    Authors

    Z. H. Qu;J. Dorsey

    Comments

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    Abbreviated Journal Title

    Int. J. Control

    Keywords

    Uncertain Dynamical-Systems; Riccati Equation Approach; Stabilizing; Controllers; Ultimate Boundedness; Matching Assumptions; Linear-Systems; Absence; Automation & Control Systems

    Abstract

    A new method of designing a robust control law is proposed for a general class of non-linear or linear systems with bounded uncertainties. The method uses the property that the Lyapunov function is not unique for a stable or stabilizable system. It is shown that the proposed control law normally guarantees the stability of the system if there are two Lyapunov functions whose null sets have a trivial intersection. The null set of a Lyapunov function is defined to be the set in state space in which the product of the transpose of the system input matrix and the gradient of the Lyapunov function is equal to zero. The robust control results impose no restriction on the structure and size of the input-unrelated uncertainties. Moreover, it is shown that asymptotic stabilization of the nominal system is not necessarily required in this method.

    Journal Title

    International Journal of Control

    Volume

    55

    Issue/Number

    6

    Publication Date

    1-1-1992

    Document Type

    Article

    Language

    English

    First Page

    1335

    Last Page

    1350

    WOS Identifier

    WOS:A1992JD82000004

    ISSN

    0020-7179

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