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Bounded feedback and structural issues in linear multivariable systems

Shan, X.Y. (1992). Bounded feedback and structural issues in linear multivariable systems. (Unpublished Doctoral thesis, City, University of London)

Abstract

In this thesis, two main issues are addressed: Bounded state feedback and evaluation of structural characteristics of large scale systems with ill-defined models.

The problems related to bounded state feedback are the closed-loop eigenvalue mobility and stabilisability of an unstable system when subject to bounded state feedback. Also related are the problems of developing measures for quantitative controllability and measures for the distance of an unstable polynomial from stability as well as the root distribution of summation of polynomials. The mobility of the closed-loop eigenvalues and the stabilisability of unstable systems are studied via the investigation of root distribution of bounded coefficient polynomials. In this thesis, direct and inverse root inclusion problems are defined and results are obtained for different class of polynomials. Then the bound on the state feedback gain is transformed into the bound on the coefficients of the closed-loop characteristic polynomials and then necessary and sufficient conditions for closed-loop eigenvalue mobility and stabilisability are derived.

The problems of evaluating the structural characteristics of large scale systems with ill-defined mathematical models are also studied. The working model characteristics and the desirable features of control theory concerning the design of large scale processes with ill-defined models have first been discussed. Next, the useful indicators for integral stabilisability and integral controllability based on the steady-state gain information are discussed. Large scale systems with structural models are then introduced and the concepts of structural McMillan degree, poles and zeros both finite and at infinity are defined. The evaluation of the structural McMillan degree, the zeros and poles both finite and at infinity are translated into finding the paths of minimum or maximum weight of integer matrices. Algorithms are also proposed and assessed.

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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