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Optimal H2/l1 control via duality theory

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1 Author(s)
Voulgaris, P.G. ; Coordinated Sci. Lab., Illinois Univ., Urbana, IL, USA

In this paper we consider the problem of minimizing the H2 -norm of the closed-loop map while maintaining its l1-norm at a prescribed level. The problem is analyzed in the case of discrete-time, SISO closed-loop maps. Utilizing duality theory, it is shown that the optimal solution is unique, and, in the nontrivial case where the l1 constraint is active, the optimal solution has a finite impulse response. A finite step procedure is given for the construction of the exact solution. This procedure consists of solving a finite number of quadratic programming problems which can be performed using standard methods. Finally, continuity properties of the optimal solution with respect to changes in the l1-constraint are established

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Automatic Control, IEEE Transactions on  (Volume:40 ,  Issue: 11 )