Abstract
This paper reports the solution of the Linear-Quadratic optimal control problem with partial stabilization constraint (LQPS) for the class of exponentially stabilizable infinite-dimensional semigroup state-space systems with bounded sensing and control having their transfer functions with entries in the algebra Bˆ, (Callier and Desoer, 1978 and 1980), extending the class of proper rational functions. This is an extension of the finite-dimensional paper of (Callier, 1984). The solution of the LQPS problem is given using spectral factorization and a diophantine equation: this is similar to (Callier and Winkin, 1990).
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