Systematization of Control Theory and Design Methods of Time-Delay Systems

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Finite spectrum assignment method for systems with delays in inputs and/or outputs was presented. Robustness of the control systems with mismatch between nominal values and actual parameters was numerically examined and it was shown that the position of integrator and the structure of observer and the state predictor change the robust stability even though poles of the closed-loop system are equal.Finite spectrum assignment methods for retarded systems with delays in state variables was presented. The characteristic polynomial of the feedback system is given by the form. * sI-A(z)-b(z)f(z) * =s^n+alpha_1(z)S^<n-1>+・・+alpha_n(z)-f(z)M(z)v(s), where z denotes the delay operator. For arbitrary real numbers beta_1, ・・, beta_n, let f(z)=[beta_n-alpha_n(z), ・・, beta_1-alpha_1(z)]M(z)^<-1>, then the characteristic polynomial becomes * sI-A(z)-b(z)f(z) * =s^n+beta_1s^<n-1>+・・+beta_n. To implement the control, an algorithm to transform f(z) into the matrix f(z,s) with polynomials in z and the f … More inite Laplace transforms was presented on the basis of the structure of M(z). Furthermore, a method to transform F(z) into F(z,s) for multi-input case was proposed by using the Smith form.In the design method by transformation the polynomial matrix in z to finite Laplace transform matrix, the calculation is required whenever beta_i are changed. To avoid the computation, a method to find K(z,s) satisfying K(z,s)M(z)v(s)=v(s) was presented in the basis of the equation M(z)v(s)=P(s)v(z) and the structure of M(z). The feedback matrix is given by f(z,s)=[beta_n-alpha_n(z), ・・, beta_1-alpha_1(z)]k(z,s).Finite spectrum assignment of systems with a class of non-commensurate delays was presented. Stabilization of systems with non-commensurate delays was also proposed on the basis of finite spectrum assignment.A solution to finite spectrum assignment problem of neutral systems was presented. In the first step, the neutral system is changed to the quasi-retarded system by using the feedback containing the delayed derivative feedback. In the second step, the finite spectrum assignment method of retarded systems is applied to the quasi-retarded ones.Finite spectrum assignment method was applied to stabilization of the repetitive control systems.Robust adaptive control for systems with mismatch between nominal delay and actual one was presented. Less