Finite Frequency H_? Filtering And Fault Detection For Spatially Interconnected Systems With Interconnected Chains

Spatially interconnected systems(SISs)with interconnected chains is a kind of multi-dimensional system with spatial distribution characteristics.SISs with interconnected chains have been widely used in many practical applications,such as automated highway systems,airplane formation flight and satellite constellations.In addition,the control system usually needs to meet different performance indicators in different frequency ranges since the characteristics of the controlled object and the spectral characteristics of the input signal have to be considered in practical control problem.Thus,many control problems can be viewed as analysis and design issues of finite frequency specifications The generalized Kalman-Yakubivich-Popov(KYP)lemma,which was developed in the last decade,is one of a straightforward and effective way to deal with finite frequency domain specifications.In recent years,the generalized KYP lemma has attracted a wide interest since it was regarded as a bridge between the frequency domain method(transfer function)and the time domain method(state space).This dissertation investigates the generalized KYP lemma for SISs with interconnected chains,and further considers the finite frequency H? filtering and finite frequency fault detection problems.The main research work of this dissertation is stated as follows:1.According to the connection characteristics between subsystems of SISs with interconnected chains,a multi-dimensional(N-D)hybrid Roesser model has been presented to describe the SISs with interconnected chains.Furthermore,note that arbitrary frequency intervals can be characterized by complex sets.In this way,a unified generalized KYP lemma for N-D(continuous,discrete,hybrid)Roesser model has been given.Bused on the generalized KYP lemma,the problem of finite frequency H? filter for SISs with interconnected chains is studied.By virtue of Finsler lemma,LMI-based method is proposed for the design of finite frequency H? filters.2.Sufficient conditions of asymptotically stability for linear two-dimensional(2-D)state-delay Roesser systems with smooth bounded initial conditions are developed using a 2-D quadratic Lyapunov function and LMI.Moreover,the generalized KYP lemma is extended to 2-D state-delay Roesser systems.The developed generalized KYP lemma can be used for continuous,discrete,continuous-discrete settings in a unified manner.The delay-dependent finite frequency bounded real lemma and finite frequency positive real lemma are investigated as the important corollaries of the delay-dependent generalized KYP lemma.Based on the above results,the problem of finite frequency robust H?,filter for uncertain 2-D continuous-discrete state-delay Roesser systems is studied.By virtue of Finsler lemma,LMI-based method is proposed for the design of finite frequency H?filters.3.The design of the finite frequency H_/H? fault detection observer for spatially interconnected time-delay systems(SITSs)with interconnected chains is investigated.The generalized KYP lemma is further extended to SITSs with interconnected chains.Bused on the developed generalized KYP lemma and the Finsler lemma,a fault detection observer is designed to guarantee the residual error system be asymptotically stable with smooth bounded initial conditions,be sensitive to the fault and be robust to the disturbances.4.The problem of finite frequency H? filtering for SITSs with interconnected chains is studied.A finite frequency bounded real lemma for SITSs with interconnected chains is proposed.Using the obtained finite frequency bounded real lemma and Finsler lemma,a finite frequency H? filter design method is derived by solving a set of linear matrix inequalities(LMIs).