| Decoupling reduces the connection among various aspects of a system, so it is convenient to study some complex performances of the system. For normal linear systems, modal decoupling problems have been studied by a lot of researchers, and a series of theories about these problems have been established. Since generalized system models arise widely in practical applications, it is desirable that some superior performances of normal systems can be generalized to generalized systems so that the performances of generalized control systems can be improved. In this dissertation, modal decoupling concepts of normal linear systems are extended to generalized linear systems, and, based on eigenstructure assignment approach, the modal decoupling control problem and the robust modal decoupling control problem in generalized linear systems are studied. The main works done in the dissertation are as follows:1. The problem of modal decoupling control for descriptor linear systems is considered. The modal decoupling conditions for generalized linear systems with zero inputs are proposed. Based on eigenstructure assignment approaches for generalized linear systems by state feedback, parametric expressions for the closed-loop eigenvectors and the feedback gain matrices are presented. Algorithms for the modal decoupling control problem in generalized linear systems are also proposed. Three numerical examples are given to illustrate effectiveness of the proposed algorithms.2. Using the criterion of minimum eigenstructure assignment condition error,the problem of robust modal decoupling control for descriptor linear systems with parameter perturbations is considered. Based on the proposed parametric solutions to the modal decoupling control problems in generalized linear systems, the robust modal decoupling control problem is turned into a minimization problem with constraints. An algorithm is then proposed. A numerical example is given to illustrate effectiveness of the proposed algorithm. |
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