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l^{1} -optimal feedback controllers for MIMO discrete-time systems

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2 Author(s)
Dahleh, M.A. ; Rice University, Houston, TX, USA ; Pearson, J., Jr.

The problem considered in this paper is the design of a closed-loop system consisting of a MIMO discrete-time plant and compensator in such a way that the system is internally stable and optimally tracks all persistent bounded inputs. The solution consists of two parts: first the calculation of the minimum value of the performance index (a weighted transfer function), which is done by solving a linear programming problem; and second, construction of the optimal transfer function by solving a set of linear equations. It is shown that, in general, the discrete-time problem will have a rational solution and thus appears to be of considerable practical significance.

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Automatic Control, IEEE Transactions on  (Volume:32 ,  Issue: 4 )