Linear periodic systems
orbit transfer problem
Springer Online Journal Archives 1860-2000
Abstract A method is developed for the approximate design of an optimal state regulator for a linear periodically varying system with quadratic performance index. The periodic term is taken to be a perturbation to the system. By making use of a power-series expansion in a small parameter, associated with periodic terms, a set of matrix equations is derived for determining successively a feedback gain. Given periodic terms of a Fourier-series form, explicit solutions are obtained for those matrix equations. A sufficient condition for existence and periodicity of the solution is also shown. Further, the performance degradation resulting from a truncation of the power-series solution is investigated. The method may effectively be used in a computer-programmed computation.
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