Stability Analysis And Distributed Control And Filtering For Time Delay Systems Interconnected Over An Undirected Graph

In recent years,systems interconnected over an undirected graph consisting of spatially or wirelessly interconnected units or subsystems with interaction and cooperation,such as unmanned aerial vehicles formation fight or satellites constellations,automated highways as well as communication networks,have been attracted considerable attention for their potential in practical applications.Time delay and Markov jump,which usually lead to instability,oscillation and poor performance,are very common in practical dynamical systems.In this thesis,we consider the stability analysis and distributed control problem for the class of time delay systems interconnected over an undirected graph.The outline of the thesis is as follows:1.For time delay systems interconnected over an undirected graph with state timeinvariant delay,the delay-independent stability and distributed control problems have been considered.The definitions of well-posedness,stability and contractiveness with respect to the plant are given.Sufficient conditions have been first developed on the wellposedness,delay-independent stability and contractiveness for the plant in terms of linear matrix inequalities.A sufficient condition is developed on the existence of a distributed output-feedback controller which inherits the structure of the plant and ensure the closedloop system to be well-posed,delay-independent stable and contractive.An algorithm is also proposed for designing an appropriate controller.Finally,numerical simulations are given to illustrate the effectiveness and feasibility of the proposed design methods.2.For time delay systems interconnected over an undirected graph with state timeinvariant delay,the delay-dependent stability and distributed filtering problems have been considered.Sufficient conditions have been developed on the well-posedness,delaydependent stability and contractiveness for the plant.And then,the filtering problem,i.e.the problem is to design distributed filter such that the filtering error system is wellposed,delay-dependent stable and contractive,is investigated.A sufficient condition on the existence of such a filter is presented in terms of linear matrix inequalities,which provides an effective way to obtain an appropriate filter inheriting the same graph as the plant.Finally,numerical simulations are given to illustrate the effectiveness and feasibility of the proposed design methods.3.For Markov jump time delay systems interconnected over an undirected graph with state time-invariant delay,the problems of delay-dependent stochastic stability analysis and distributed filter synthesis have been considered.A sufficient condition for the well-posedness,delay-dependent stochastic stability and contractiveness of the plant is developed in terms of linear matrix inequalities.The distributed filter synthesis aims to design a distributed filter inheriting the structure of the plant such that the filtering error systems is well-posed,delay-dependent stochastically stable and contractive.Using Fisher Lemma,a sufficient condition on the existence of such a distributed filter is proposed via a serious of finite-dimensional linear matrix inequalities.Finally,a numerical simulation is presented to demonstrate the effectiveness of the proposed approach.4.For Markov jump time delay systems interconnected over an undirected graph with state time-varying delay,the problems of stochastic stability analysis and distributed output-feedback controllers design have been considered.A sufficient condition for the well-posedness,stochastic stability and contractiveness of the resultant closed-loop system is first developed in the form of non-linear matrix inequalities.Then,to avoid the difficulty of solving non-linear matrix inequalities,the sufficient condition is relaxed to an equivalent one in terms of coupling linear matrix inequalities,which provides an effective way to confirm the existence of a distributed output-feedback controller inheriting the structure of the given plant.Furthermore,a constructive algorithm is given for the design of such a distributed output-feedback controller.Finally,numerical simulations are given to illustrate the validity of the proposed method.5.For Markov jump time delay systems interconnected over an undirected graph with state time-varying delay,the problems of stochastic finite-time stability analysis and distributed finite-time control have been considered.Firstly,the concepts of finite-time stochastic finite-time boundedness and contractiveness for the class of systems are given.Then,a sufficient condition on the well-posedness,stochastic finite-time boundedness and contractiveness for the resulting closed-loop systems is proposed by a set of nonlinear matrix inequalities in some given finite-time interval.For decoupling this non-linearity,a sufficient condition on the existence of a mode-dependent distributed dynamic output feedback controller is established in terms of linear matrix inequalities with some fixed parameter.Furthermore,an algorithm is presented to obtain the parameters of such controllers.Finally,a numerical simulation is presented to show the validity of the proposed method.