Abstract
Abstract A design method based on pole assignment considerations for an nth order linear time-invariant single-input p-output system by means of static (constant gain) feedback is presented for the case in which the rank p of an output matrix C is less than the number of system states n. The constraints in pole assignment are described in the form of linear relationships between the coefficients of the closed-loop characteristic polynomial and some open-loop system parameters. It has been shown that the problem of pole assignment is equivalent to the problem of solving a set of n linear equations with p unknowns in such a way that n – p equations are made linearly dependent by proper choice of coefficients of the closed-loop characteristic polynomial. As a result, all n system poles can be shifted to selected locations which satisfy the constraints. Of particular interest are the design methods for the cases when the number of arbitrarily assigned poles are equal to p and p – I.
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