A new approach to the design of time-varying control systems with application to the Space Shuttle Boost
A general approach to the analysis and design of closed-loop control for slowly time-varying linear systems is presented. The approach uses the method of generalized multiple scales in which slow and fast dynamics are systematically separated by employing different 'clocks' which measure time at varying rates. The clocks, which are necessarily nonlinear functions of time, are chosen in such a manner that the system dynamics are asymptotically invariant with respect to the new time scale. A transfer function relating the output to the input for general linear slowly time-varying systems is developed and represents the actual system under certain conditions. The clock function is shown to satisfy an algebraic characteristic equation and can be determined in terms of the coefficients. The approach can be viewed as an extension of time-invariant linear feedback control theory.