Robust state observer and control design using command-to-state mapping

    Authors

    Z. H. Qu

    Comments

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    Abbreviated Journal Title

    Automatica

    Keywords

    robust observer; robust nonlinear control; robust state estimation; observer Lyapunov function; Lyapunov direct method; Lyapunov stability; matrix Lyapunov equation; generalized algebraic Lyapunov equation; Jacobian matrix; UNCERTAIN DYNAMIC-SYSTEMS; NONLINEAR-SYSTEMS; OUTPUT-FEEDBACK; STABILIZATION; Automation & Control Systems; Engineering, Electrical & Electronic

    Abstract

    In this paper, by introducing the concept of command-to-state/output mapping, it is shown that the state of an uncertain nonlinear system can robustly be estimated if command-to-state mapping of the system and that of an uncertainty-free observer converge to each other. Then, a global Jacobian system is defined to capture this convergence property for the dynamics of estimation error, and a set of general stability and convergence conditions are derived using Lyapunov direct method. It is also shown that the conditions are constructive and can be reduced to an algebraic Lyapunov matrix equation by which nonlinear feedback in the observer and its corresponding Lyapunov function can be searched in a way parallel to those of nonlinear control design. Case studies and examples are used to illustrate the proposed observer design method. Finally, observer-based control is designed for systems whose uncertainties are generated by unknown exogenous dynamics. (C) 2005 Elsevier Ltd. All rights reserved.

    Journal Title

    Automatica

    Volume

    41

    Issue/Number

    8

    Publication Date

    1-1-2005

    Document Type

    Article

    Language

    English

    First Page

    1323

    Last Page

    1333

    WOS Identifier

    WOS:000230449000003

    ISSN

    0005-1098

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