State Observer Design For A Class Of Linear Time-varying Systems

In this paper,linear state observer design of linear time-varying systems has been researched to solve the state reconstruction problem that states cannot be acquired compeletely or partialy due to various reasons in actual engineering.Different from the mature theory of state observer for linear time-invariant systems,research on linear time-varying systems is ralatively more difficult and challenging,less amount of theoretical achievements and closer to the actual project.So it is the research focus in recent years.The main contents of this paper are described below.Design ideas of this paper is to transform the original linear time-varying systems into some special form with linear non-singular transformations initially.Then the state observer design based on the linear time-varying systems transformed can achieve the reconstructed state of original linear time-varying systems.For this idea,we can know that the design work is divided into two parts,namely,linear nonsingular transformation and state observer design.Firstly,the state observer design of linear time-varying systems based on the square matrices is presented.The coefficient matrices of systems transformed are all partitioned including much zero and unit submatrices.Then the full,reduced and Luenberger state observer design of transformed systems are illustrated detailed including some aspects such as the solutions of dynamis equations and coefficient matrices,as well as the algorithms and their steps.Secondly,we propose the state observer design for linear time-varying systems based on row expansion.The linear nonsingular transformation matrix is obtained by computing the linearly independent rows of observation matrix.The coefficient matrices of transformed system are still partitioned,and the difference between two linear nonsingular metiods is that each of its sub-blocks contains much zero elements.The the full state observer is designed.Based on a design idea,all the state observers obtained by the two design methods are proved to be feasible and effective by simulation.Moreover,the contrast of two methods is proposed in this paper in order to select in actual engineering.Finally,the paper studies the separation principle of closed loop system in linear time-varying system,and obtains the conclusion that the state observer designed in this paper meets the separation principle.The main research results of the paper is to promote and increase theoritical achienements of the state observer design for linear time-varying systems.The pivotal merit is that it can avoid solving complex differential equations by transforming them into constant partially.These reduces and simplifies the computational complexity as well as the amount of computation greatly.Therefore,they also have practical engineering significance.