Robust stabilization of linear time-invariant uncertain systems via Lyapunov theory

This dissertation is concerned with the problem of synthesizing a robust stabilizing feedback controller for linear time-invariant systems with constant uncertainties that are not required to satisfy matching conditions. Only the bounds on the uncertainties are required and no statistical property of the uncertainties is assumed. The systems under consideration are described by linear state equations with uncertainties. I.e. x(t) = A̅(γ)x(t) +B̅(γ)u(t), where A̅(γ) is an n x n matrix and B̅(γ) is an n x m matrix. Lyapunov theory is exploited to establish the conditions for stabilizability of the closed loop system. We consider a Lyapunov function with an uncertain symmetric positive definite matrix P. The uncertain matrix P satisfies the Lyapunov equation A^TP + PA + Q = 0, where the matrix A is in companion form and the matrix Q is symmetric and positive definite. In the solution of the Lyapunov equation, m rows of the matrix P are fixed in our approach of designing a robust controller. We derive necessary and sufficient conditions on these fixed m rows of the matrix P such that for given positive definite and symmetric Q the solution of the Lyapunov equation yields a positive definite matrix P and a companion matrix A that is Hurwitz. A discontinuous robust stabilizing controller is given. Linear controller design is also investigated in this research. Under the same assumptions for the existence of a stabilizing discontinuous controller, we show that a linear robust stabilizing controller always exists. The dissertation includes three examples to illustrate the design procedures for robust controllers. Example 2 shows that the design procedure may be applied to time-varying nonlinear systems.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Aerospace and Ocean Engineering

Department dc:contributor.department

Aerospace and Ocean Engineering

Grantor dc:publisher

Virginia Polytechnic Institute and State University

Year dc:date.issued

1988

Author dc:creator

• Chao, Chien-Hsiang

Chair dc:contributor.committeechair

• Stalford, Harold L.

Committee members dc:contributor.committeemember

• Cliff, Eugene M.
• Lutze, Frederick H.
• Hendricks, Scott L.
• Burns, John A.

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en_US

Handle dc:identifier.uri

http://hdl.handle.net/10919/53928

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/53928