Robust Performance Analysis And Distributed Control Of Systems Interconnected Over An Arbitrary Graph

The interconnected system is a large-scale system which consists of multiple subsystems interconnected over an undirected graph.One of the most particular features of the intercon-nected system is that each subsystem can detect,compute and actuate locally,and moreover,cooperate with neighboring subsystems to accomplish a desirable task by sharing information through the network.Due to the broad range of practical applications in Power system,robot formation system,automatic highway system,satellite networking system and other areas,the interconnected systems have received significant attention.This dissertation mainly studies the H₂performance analysis andH₂distributed controller design problem,generalized Kalman-Yakubovich-Popov lemma,finite frequencyH_∞filtering and distributed static output feedback control design problem of the continuous-time interconnected system.This dissertation also studies the finite frequencyH_∞performance analysis and distributed filter design problem,robust finite frequencyH_∞distributed memory filter design problem of the discrete-time inter-connected system.The main work of this dissertation includes:（1）TheH₂performance analysis andH₂distributed controller design problem are con-sidered for the continuous-time interconnected system.The classical definition of theH₂per-formance of one-dimensional linear system is extended to the interconnected system for the first time.A sufficient condition for the well-posedness,asymptotic stability and evaluating the H₂performance of the interconnected system is presented in this paper and this condition is in terms of individual subsystems.Moreover,a sufficient condition is given for the existence of theH₂distributed output-feedback controller and a constructive method is then presented for the design of optimalH₂distributed controller.A practical example is included to illustrate the applicability and effectiveness of the proposedH₂distributed control design methodology.（2）The generalized Kalman-Yakubovich-Popov（KYP）lemma and its application in finite frequencyH_∞distributed filter design are considered for the continuous-time interconnected system.The network communication channels between subsystems are considered to be af-fected by uncertainties.Firstly,based on the proposed linear matrix inequality characterization for an finite frequency region and S-procedure,a generalized KYP lemma is presented for the interconnected system.After that,the finite frequency bounded realness and finite fre-quency positive realness in terms of individual subsystems are studied as special cases of the proposed generalized KYP lemma.Moreover,as an application of the developed generalized KYP lemma,the finite frequencyH_∞distributed filtering problem for the non-ideally intercon-nected system is studied.Finally,illustrative examples are given to show the effectiveness of the proposed method.（3）The distributed static output feedback（DSOF）controller design problem is consid-ered for the continuous-time interconnected system in finite frequency domain.By introducing some dilated multipliers into the extended condition that guarantees the well-posedness,sta-bility and finite frequencyH_∞performance of non-ideally interconnected systems,we derive a new equivalent condition,which is more effective for parameterizing the DSOF controller.A two-stage approach is then developed for constructing a DSOF controller:design an initial distributed full information（DFI）controller first and then derive a desired DSOF from the DFI controller.Moreover,two iterative linear matrix inequality based algorithms are proposed to improve the solvability of the DFI controller and DSOF controller design problems.Finally,an example is given to show the effectiveness of the proposed two-stage DSOF controller design method.（4）The finite frequency bounded realness analysis and finite frequencyH_∞distributed filter design problem are considered for the discrete-time interconnected system.TheH_∞per-formance analysis of networked systems is generalized from the entire frequency region to some finite frequency regions.A necessary and sufficient condition in the centralized manner is established to check the finite frequency bounded realness property of the interconnected system.Moreover,in order to design a distributed filter and reduce the computational effort,a sufficient condition in terms of individual subsystems is developed.Based on the new con-dition derived,a sufficient condition is given for the existence of the distributed filter and an LMI method is then presented for designing the distributed controller.A practical example is included to illustrate the proposed approach.（5）The robust finite frequencyH_∞distributed filtering problem is considered for uncertain discrete-time interconnected system.By using past output measurements and considering the frequency information of disturbance signals,the designed distributed memory filter is able to guarantee that the filtering error system is well-posed,stable and satisfies the finite frequency H_·performance.Based on the extended finite frequency bounded realness lemma for the un-certain interconnected system,the existence condition of robust finite frequencyH_∞distributed memory filter is derived.Moreover,it is shown that by taking advantage of more past out-put measurements of the interconnected system,the proposed design procedure can derive a distributed filter that achieves a lowerH_∞performance bound.Finally,a practical example is given to show the effectiveness of the proposed filter design method.