Parametric Control Design For Descriptor Linear Systems

Descriptor system is a kind of dynamic systems of more general and abroad applied background, and has attracted much attention in the last three decades. Considering the linear time-invariant descriptor systems, the work of this dissertation mainly addresses the issues of parametric control design for descriptor linear systems, which include eigenstructure assignment, robust pole assignment and model reference control. The major contributions of the dissertation are as follows:1. The generalized Sylvester matrix equation AV + BW = EV J is considered. First, a new explicit parametric solution of the matrix equation is proposed. Second, an existing solution of this matrix equation is extended. The obtained solutions lay a foundation for design of descriptor linear systems using parametric approaches.2. First, the problem of eigenstructure assignment via state feedback in R-controllable descriptor linear systems is considered. Based on the new explicit parametric solution to the generalized Sylvester matrix equation, a parametric approach for eigenstructure assignment via state feedback is proposed. The proposed approach is easy to compute and possesses good numerical property. Second, the problem of eigenstructure assignment in R-controllable and -R-observable descriptor linear systems via output feedback is considered. Based on the new explicit parametric solution to the generalized Sylvester matrix equation, a parametric approach for eigenstructure assignment via output feedback is proposed. The proposed approach is easy to compute and possesses good numerical property. Finally, the problem of eigenstructure assignment via state feedback in -R-stabilizable descriptor linear systems is considered. Based on the extended solution to the generalized Sylvester matrix equation, a parametric approach for eigenstructure assignment via state feedback is proposed. This approach is an extension of the results of eigenstructure assignment via state feedback in R-controllable descriptor linear systems.3. The problem of robust eigenstructure assignment via state feedback in descriptor linear systems with parameter uncertainties is investigated. The design criterion is to minimize the error in the set of equations which govern the closed-loop eigenvalues and eigenvectors. Based on an eigenstructure assignment result for descriptor linear systems via state feedback, a general parametric expression of the robust index is proposed, and a simple effective optimization algorithm for robust eigenstructure assignment via state feedback in descriptor linear systems is then given.4. Based on an eigenstructure assignment result for descriptor linear systems via output feedback and a sensitivity result of generalized eigenvalues of matrix pairs, the problem of robust eigenstructure assignment via output feedback in descriptor linear systems is considered. General parametric expressions of the closed-loop eigenvalues sensitivities to the perturbed elements in the open-loop system matrices are obtained, and a simple effective algorithm for robust pole assignment via output feedback in descriptor linear systems is then proposed.5. Based on an eigenstructure assignment result for descriptor linear systems via proportional plus partial derivative state feedback and a sensitivity result of generalized eigenvalues of matrix pairs, the problem of robust eigenstructure assignment via proportional plus partial derivative state feedback in descriptor linear systems is solved. General parametric expressions of the closed-loop eigenvalues sensitivities to the perturbed elements in the open-loop system matrices are obtained, and a simple effective algorithm for robust pole assignment via proportional plus partial derivative state feedback in descriptor linear systems is then proposed.6. First, the problem of model reference control for descriptor linear systems is considered. A model reference zero-error asymptotic tracking controller is established. The controller is composed of two parts: one is the feedback of the measurement output of the controlled plant; the other is the feedforward of the input and state of the reference model system. Based on a complete parametric solution to the generalized Sylvester matrix equation, the general complete parametric expression for the controller is presented and a simple effective algorithm is then proposed. Second, based on the proposed model reference asymptotic tracking controller the problem of robust model reference control for descriptor linear systems subject to parameter uncertainties is considered. The problem is decomposed into two separate problems: a robust stabilization problem and a robust compensation problem. A simple effective algorithm for solving these two separate problems is then proposed.