The RCF For Continuous-time Uncertain Systems

Coprime factorization approach is very popular for model redoction.In recent years,there has been growing interests in model reduction problems for uncertain systems.So coprime factorization approach become more and more important.The blanced tryncation methods can guarantee robust stability of the reduced systems and yield bouds on model reduction errror from an input-output perpective.However,the original uncertain systems are required to satisty certain robust stability conditions to proceed with tne balanced truncation approaches.This requirement prevents it application to those uncertain systems which may be robustly unstable.One of the common solutions,for the nominal liner time invariant systems,to overcome this difficulty is to use the coprime factor approach.This approach is then extended to discrete-time uncertain systems to obtain reduced-order uncertain systems with guaranteed error bouds on the derived coprime factors,and in some papers they consider coprime factorization for LPD.This motivates us to seek for a coprime factor model reduction method for continuous-time uncertain systems.L.Li has showed the contractive RCF for the continuous-time uncertain systems.More deeply in this paper we will discuss the expansive RCF for the continuous-time uncertain systems.In this paper,we consider a class of continuous-time uncertain systems.The main aim of us is to obtain the expansive right coprime factorization for the system.A systematic approach is presented to construct an expansive coprime factorization for the continuous-time uncertain system,based on the use of liner matrix inequalities and Schur completment.This method is applicable to the uncertain systems which may be robustly unstable,overcoming the robust stability restriction in the balanced truncation approach.The details will be discussed in the future.Error bound of the resulting coprime factor is derived on the L₂-induced norm.