Reduced-order Filter Design Based On LMI

It attracted quite some attention to design the reduced-order filters to reduce the numerical complexity and computational burden of the real-time filtering process over the past decade.In this dissertation,the reduced-order filter design methods are investigated.The main contributions of this dissertation are as follows.Firstly,we consider reduced-order H_∞filtering design for continuous singular systems.By adding a complementary constraint,the original system is divided into a nominal system and an uncertain part,then the stable invariant zeros of the original system become unstable in the nominal system.Based on the nominal system,a reduced-order H_∞filter can be designed for the original system by using the existing method.One major contribution of the present work is that a new upper bound of order reduction is proposed,an algorithm to solve the problem of reduced-order H_∞filtering is given,and the range of invariant zeros which can be used to construct a reduced-order H_∞filter is discussed.An illustrative example is given to demonstrate the effectiveness of the proposed approach.Secondly,we consider the design algorithms of reduced-order L₂-L_∞filtering of linear time-invariant continuous systems.It is known that the solvability of the reduced-order L₂-L_∞filtering problem is characterized in terms of linear matrix inequalities(LMIs) and a coupling non-convex rank constraint.The problem becomes a non-convex optimal problem because of the coupling non-convex rank constraint. We adopt constructive method to deal with this non-convex optimal problem.One major contribution of the present work is that a new upper bound of order reduction is proposed,and an algorithm to solve the problem of reduced-order L₂-L_∞filtering is given.A sample example is given to show the efficiency of the proposed approach.Finally,we consider the design of reduced-order robust H_∞filtering for linear system with parameter uncertainties,which lays the fact that the norm is limitary.The problem above can be changed to the reduced-order H_∞filtering design for a new system,which can be used to design a reduced-order filtering by using the existing methods.