• Analysis and control of time-periodic systems with time delay via chebyshev polynomials

      Ma, Haitao (2003-08)
      A technique for studying the transient response and the stability properties of dynamic systems modeled by delay-differential equations (DDEs) with time-periodic parameters is presented in this thesis. The approach is based on an orthogonal polynomial expansion (shifted Chebyshev approximation). In each time interval with length equal to the delay period, the dynamic system can be reduced to a set of linear difference equations for the Chebyshev expansion coefficients of the state vector in the previous and current intervals. In this way, the transient response of the dynamic system can be directly obtained and the stability properties are found to be determined by a linear map which is the "infinite-dimensional Floquet transition matrix". The technique is then used to study the stability of an elastic system subjected to periodically-varying retarded follower forces, solve a finite horizon optimal control problem via quadratic cost function, and design a delayed feedback controller by using both numerical and symbolic approaches to control the chaotic behavior of a nonlinear delay differential equation.