Heusden, E. van (1999) On generic pole assignment of linear timeinvariant systems by memoryless periodically timevarying output feedback. Master's Thesis / Essay, Mathematics.

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Abstract
It was shown by Wonham that the closedloop poles of a linear timeinvariant 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 timeinvariant 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 timevarying controllers.
Item Type:  Thesis (Master's Thesis / Essay) 

Degree programme:  Mathematics 
Thesis type:  Master's Thesis / Essay 
Language:  English 
Date Deposited:  15 Feb 2018 07:28 
Last Modified:  15 Feb 2018 07:28 
URI:  http://fse.studenttheses.ub.rug.nl/id/eprint/8621 
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