Abstract
A problem of H/sub 2/ optimization via state feedback is considered. The problems dealt with are of the general singular type, with a left invertible transfer matrix function from the control input to the controlled output. All the static and dynamic H/sub 2/ optimal state feedback solutions are constructed and parameterized, and all the eigenvalues of an optimal closed-loop system are characterized. All optimal closed-loop systems share a set of eigenvalues which are termed the optimal fixed modes, which must be assigned among the closed-loop eigenvalues. This set includes a set of optimal fixed decoupling zeros which shows the minimum absolutely necessary number and location of pole-zero cancellations present in any H/sub 2/ optimal design. It is shown that both the sets of optimal fixed modes and optimal fixed decoupling zeros do not vary. >
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