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Algebraic synthesis methods for linear multivariable systems: Decentralized stabilization

Wilson, D.R. (1990). Algebraic synthesis methods for linear multivariable systems: Decentralized stabilization. (Unpublished Doctoral thesis, City, University of London)

Abstract

A unifying approach for the study of solvability of algebraic synthesis problems defined on linear time invariant multivariable systems is given. The decentralized stabilization problem is formulated over the ring of proper and stable rational function and its solution reduces to the study of (sets of) matrix equations of the type AX = B. It is shown that many control problems can be described algebraically using matrices defined over special rings. The rings of importance are the Euclidean domains R[s] , Rpr(s) and Rp(s) and these are used to investigate the structural and invariant aspects of system stability equations. The solvability of AX = B also provides conditions for the solvability of the generalised Diophantine equation.

The Diagonal Stabilization Problem (DSP) is defined over the ring of proper rational functions which have no poles inside a prescribed region of the finite complex plane. Solvability is intimately related to systems which exhibit the property of cyclicity. Necessary and sufficient conditions are established for the existence of solutions to the DSP. A complete parameterization of stabilizing controllers for 2x2 case is given. Conditions of nonsolvability and hence nonstabilizability yield an explicit expression for the fixed modes of the system.

The algebraic tools are given to investigate special type solutions such as realisable, stable and performance related controller designs as well as the more general case of multi- channel systems.

Publication Type: Thesis (Doctoral)
Subjects: Q Science > QA Mathematics
T Technology > TA Engineering (General). Civil engineering (General)
Departments: School of Science & Technology > Engineering > Electrical & Electronic Engineering
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