The Parameter Dissipation Condition Analysis Of Time-Delay Systems

In this paper,the stability of four-neuron bidirectional annular multi-time delay neural network system and the hyperbolic partial differential equations(systems)with non-homogeneous perturbations is studied.Firstly,we discuss the delay-dependent and delay-independent on the stability of a bidirectional ring neural network system.Secondly,the stability of the hyperbolic partial differential equations(systems)under the proportional integral(PI),proportional integral differential(PID)and the linear combination of instantaneous position and time-delay position(PDP)feedback control laws is analyzed.The first chapter describes the research background,significance,research progress and research content of the control problem of infinite-dimensional coupled system.In the second chapter,we study the stability of a bidirectional ring neural network with four neurons and three delays.Firstly,the system is linearized near the equilibrium point,and its characteristic equation is obtained by multiplying the series of four first-order exponential polynomials.Secondly,based on the distribution of zeros of exponential polynomial and the method of eigenvalue analysis,the sufficient conditions of parameters to ensure the stability of the system are discussed,and the critical values of three delay parameters are given.In the third chapter,the stability of hyperbolic partial differential equations(systems)with non-homogeneous perturbations under PI,PID and PDP boundary feedback controllers is studied.In the PI and PID controllers case,a one-dimensional hyperbolic conservation law system with non-homogeneous disturbance is analyzed.Firstly,the formal solution of the system is acquired by using the characteristic line method,which is substituted into the boundary conditions to obtain that the characteristic equations of the system are transcendental equations with a single exponential term.Secondly,the dissipative conditions of the feedback parameters are established by using the Walton-Marshall stability criterion.For vector conservation law systems,similar methods are used to consider the conditions of the system feedback parameters under PI controller.In addition,Under the PDP controller,the characteristic equation of the system is a transcendental equation containing two exponential parameters.The distribution theorem of zero points of exponential polynomials and Schur-Cohn criterion of the inner root of the unit circle of real coefficient polynomials are used to give the value range of parameters when the system reaches stability.In the forth chapter,the stability analysis of one-dimensional hyperbolic conservation law system under PI controller is addressed.Firstly,the PDE-PDE infinite dimensional coupling system is reconstructed.Secondly,the well-posedness of the system is proved based on the operator semigroup theory.Finally,the characteristic equation of the system is calculated,then the stability of the closed-loop system is established by using the exponential polynomial zero distribution theorem and the characteristic root method.