Study On The Theory Of Model Reduction And Observer Of Control System

The theoretical research of model reduction and observers in control systems has always been a hot issue in the field of mathematics and engineering,especially the discussion of model reduction methods and the problem of estimating the state of dynamic systems from inputs and outputs.Based on the existing research,this paper discusses the existence of unified H_?dynamic observer,and the comparison among several common model reduction methods for linear stable time-invariant systems.The main contents of this paper include:1.The existence of unified H_?dynamic observer proposed by Nan et al[1]is studied.When the unified H_?dynamic observer exists,whether there is a solution to a set of special Sylvester matrix equations is discussed.By using the matrix theory,this paper conducts relevant derivation and demonstration,and the sufficient and necessary conditions for the solution of the Sylvester matrix equations are obtained,as well as the structure of solutions.It shortens the search range of parameters in the unified H_?dynamic observer design problem,and gives the algorithm for solving the Sylvester matrix equations.Finally,a numerical example is given to illustrate the influence of different values of parameters in the structure of the solution on the existence of unified H_?dynamic observer.2.For the H₂ optimal model reduction problem,in this paper,we first introduce the Wilson's necessary condition satisfied by the matrix parameterization method and the reduction model constructed by Galerkin's approximation method.Then,it proved that the two are essentially the same.Finally,the limitations of the Krylov subspace method are pointed out.