Finite Frequency Analysis And Robust Control Of Spatially Interconnected Systems

As a kind of large-scale systems,spatially interconnected systems(SISs)is formed by similar subsystems in the way of interconnected chains,which is also regarded as multi-dimensional system model since both temporal and spatial variables have been taken into account.Compared with the traditional two-dimensional(2-D)system models,the main feature of SISs includes that both causal and non-causal spatial operations are considered,and moreover,the dimension of spatial variables are extended to arbitrary dimensions.These characteristics give the system model a better generalization ability,but also bring substantial differences among performance analysis and control,leading to considerable attentions from scholars around the world.This dissertation is concerned with stability analysis,H∞ control,finite-frequency analysis and robust synthesis of continuous-time SISs with bi-directional interconnections.The main work of this dissertation includes the following contents:(1)The problems of stability and robust stabilization control for SISs are investigated.Firstly,necessary and sufficient conditions for the stability of SISs under different topologies are derived by resorting to rational decomposition of matrix polynomials and Routh-Hurwitz criterion.After that,the feasibility of derived stability conditions is quantified with the help of sum of squares decomposition theory and the generalized trace parameterization of real-valued trigonometric polynomials.Then,inspired the ideal of robust stabilizability function,the problem of robust output-feedback stabilization control for uncertain SISs is addressed in consideration of parameter uncertainties.In which,the parameters of stabilizing controller are designed by using the square matrix representation of the polynomial.Lastly,the efficiency of stability conditions and the robust stabilization method are demonstrated in simulation examples.(2)The robust quadratic stability and distributed H∞ control problem for spatially interconnected systems with external disturbances are studied.Firstly,the concept of robust quadratic stability of uncertain SISs is defined,and then linear matrix inequality(LMI)condition for robust quadratic stability is given based on Lyapunov stability theory of infinite dimensional systems.Then,Parseval’s theorem for SISs is established to introduce the concept of H∞ performance in frequency domain,and based on time domain analysis,a bounded real lemma that can deal with the H∞ performance index is given.Finally,robust distributed H∞ control method based on the given system matrices is studied for the uncertain SISs by means of elimination-lemma and cone-complementary linearization,and the effectiveness of the H∞ controller is verified in the example of a platoon of vehicles.(3)The problems of finite frequency distributed filtering and model reduction are studied based on the H∞ performance analysis of SISs over finite frequency domain.Firstly,the concept of H∞ performance of SISs is extended to the case of finite frequency domain in consideration of the frequency characteristic of disturbance.Then,the finite frequency bounded real lemma and its full-frequency form are given from the perspective of frequency domain,and the equivalence between the bounded real lemmas based on frequency domain analysis and time domain analysis is established.Finally,by resorting to Finsler’s lemma and weighted relaxation matrix method,H∞ filtering and model reduction methods over finite frequency domain of SISs are given,and the advantages of H∞performance analysis and synthesis in finite frequency domain are verified by simulation examples.(4)The design of finite frequency H-/H∞ fault detection observer for SISs is investigated.At first,the concept of H-performance index in finite-frequency domain is introduced into SISs to measure the minimum fault sensitivity over finite frequency domain.Then,the generalized Kalman-Yakubovich-Popov(KYP)lemma which can deal with the finite frequency H-performance index over all possible finite frequency ranges is established by exploring in great depth the complexity of finite-frequency characteristics arising from the different frequency domain ranges of each frequency variables.On this basis,H-/H∞fault detection observer,which can enhance both finite-frequency fault sensitivity and full-frequency disturbance robustness,is designed with the aids of bounded real lemma and generalized KYP lemma.Finally,the validity and superiority of the finite frequency fault detection method are verified in a simulation example.