The Dynamic Compensator Design For Linear Systems Based On Polynomial Matrix Description

From 70's 20 century, the theory of linear time-invariant systems complex frequency domain which is based on polynomial matrix had a rapid development, and formed an integrated and sophisticated modern linear systems complex frequency domain theory. Its primary characteristic is that it uses the transfer function matrix's matrix fraction description (MFD) or polynomial matrix description (PMD) as a mathematic model of systems, takes the polynomial matrix approach as the tool of the systems analysis and synthesis. In the light of recent work on the theory of linear systems complex frequency domain, this thesis provides a systematic study on the problem of determination of a minimal polynomial basis of the left kernel of a given polynomial matrix and design dynamic compensators for linear systems.The main contents are as follows:A new algorithm for the computation of a minimal polynomial basis of the left kernel of polynomial matrix is proposed. This method exploits the structure of the left null space of generalized Wolovich and Sylvester resultants to compute row polynomial vectors that form a minimal polynomial basis of left kernel of polynomial matrix. The entire procedure can be implemented using orthogonal transformations of constant matrices and results to a minimal basis with orthonormal coefficients.Some problems about the design of dynamic compensators for polynomial matrix description based linear systems, which is controllable and observable, is discussed. A number of relations which are satisfied by prime polynomial matrices are derived and then used to study the polynomial matrix equation and to parametrically characterize the class of output feedback compensators for linear systems.Under normal circumstances, the problem about the design of dynamic compensators for linear systems based on polynomial matrix description is discussed. By utilizing the relation between prime polynomial matrices, and linking the quomodo of derivate polynomial matrix equation, the general form of compensation design algorithm is given, which is shown to be effective by numerical exampleas.