A Theory of Systems Characterized by Parameters and It's Application to Control Systems

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This study is concerned with a family S of dynamical systems S(lambda) characterized by q((〕SY.gtoreq.〔) 0) real parameters lambda = [lambda_1, lambda_2, ・・・, lambda_q] in the form where X is the state space and LAMBDA * R^q is a given set. The purpose of this stydy is to describe such a family in mathematical and system theoretical terminologies, to investigate various mathematical structures of the family and to apply these results to important control problems. To simplify the development, it is assumed that each system S(lambda) is linear and depends on the parameters lambda in polynomial form, and the family S is investigated in the following two cases : (a) X is finite dimensional and (b) X is infinite dimensional.The main results obtained for cases (a) and (b) are summarized as follows.(a) For q = 1, the family S can be described as a single linear system defined over a principal ideal domain, and the disturbance decoupling problem and the block triangular decoupling problem are … More studied to obtain some solvability conditions. For q (〕SY.gtoreq.〔) 2, the family S can be represented as a single linear system over a unique factorization domain, and various control problems are examined. In particular, necessary and sufficient conditions for the block decoupling problem to be solvable are obtained. Finally, given a finite set of linear systems, various decoupling problems are considered for a system characterized as a convex combination of these systems, and some necessary and/or sufficient conditions for their solvability are proved.(b) For given two infinite dimensional systems, a system which is represented as convex combination of the two system is considered as a special case of q = 1. Some sufficient conditions for this system to be rejected from disturbance are obtained.Finally, using a symbolic manipulation system MAPLE, various computer systems are constructed to perform symbolic and numerical computations necessary for practical applications of the obtained results. Less