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On generic pole assignment of linear time-invariant systems by memoryless periodically time-varying output feedback

By E. van Heusden


It was shown by Wonham that the closed-loop poles of a linear time-invariant system can be assigned arbitrarily by real memoryless state feedback if and only the system is controllable. The use of output feedback can be a good alternative in case the state is not available for feedback. In 1992 it was proven by Wang that if n < mp (where n is the number of states, m the number of inputs and p the number of outputs), then generically the system is arbitrary pole assignable by real memoryless time-invariant output feedback. One of the proofs of this theorem is based on a behavioral approach. Another possibility for achieving pole assignment is applying periodic output feedback. Using the technique of lifting, exact conditions were derived in the literature for SISO systems, showing that, under these conditions, we have (almost) arbitrary pole placement by periodic output feedback with period T = n + 1. In this report we use this lifting technique for MIMO systems, and establish conditions on n, m,p and the period of the controller for generic arbitrary pole placement. This is achieved by formulating the pole placement problem in a behavioral context and extending the behavioral proof to periodically time-varying controllers.

Year: 1999
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