Reduced-order H_∞ Controller And Filter Design

In this dissertation, reduced-order H_∞controller and filter design methods are investigated. The main contributions of this dissertation are as follows.Firstly, we consider reduced-order H_∞filtering design for continuous descriptor systems. The purpose is to design linear filters with a specified order lower than the given system such that the filtering error dynamic system is admissible and satisfies a prescribed H_∞performance level. One major contribution of the present work is that a new upper bound of order reduction is proposed in continuous-time context. An algorithm for constructing the reduced-order H_∞filtering is given. It is known that the necessary and sufficient conditions for the solvability of this problem are characterized in terms of matrix inequalities and a coupling non-convex rank constraint. The algorithm to deal with the non-convex optimal problem is constructive, which leads to a computational method to solve the matrix inequalities. An illustrative example is given to show the efficiency of our approach.Secondly, we consider reduced-order controllers for a class of mixed H₂/H_∞control problem. There is a new controller degree bound for the H_∞control problem in terms of the minimal rank of the system matrix pencils of these two transfer function matrices in the unstable region. When the unstable invariant zero exists, this paper shows the following important result: If the mixed H₂/H_∞problem is solvable, then there must exist reduced-order controllers with orders less than that of generalized plant. Moreover, we can also give new feasible LMI-based design methods for constructing the reduced-order controller because of the constructive proof, which only involve algorithms and convex optimizatin of LMI. The result developed in this paper are valid both for the continuous- and discrete-time mixed H₂/H_∞control problems.Finally, robust reduced-order Luenberger observer-based H_∞controller design for descriptor systems is investigate. This observer is with disturbance decoupling. Firstly, a necessary and sufficient condition for the H_∞state-feedback control problem of descriptor systems is established. Then get the H_∞state-feedback gain matrixs by solving LMIs. This paper observe the H_∞state-feedback gains gradually. Based on the parametric design approach for generalized Sylvester matrix equations, the reduced-order H_∞controller design for descriptor systems is realized. One major contribution of the present work is that a design algorithm for constructing the reduced-order H_∞controller is given. An illustrative example is given to show the efficiency of our approach.