Finite-dimensional variable structure control design for systems with a single time delay

A design method for the variable structure control of point time-delay systems is studied in this paper. The proposed switching function and variable structure controller are of finite dimension. The basic idea is to construct a finite-dimensional system which contains all the unstable poles of the original time-delay system and hence those unstable poles of the time delay system will be absorbed by the developed variable structure controller. The proposed method is applied to the stabilization of combustion in a liquid monopropellant rocket motor and satisfactory results are obtained by simulation study. Smooth dependence of the closed-loop system response on the two parameters, the pressure exponent y and time lag ∞, are shown by simulation results.