article · AIP conference proceedings
In this paper, we investigate the linear quadratic problem for linear continuous-time systems of infinite-dimensional with nonnegative state constraints. We state conditions under which, the solution of the standard linear quadratic problem LQ∞ in infinite-dimensional state space is the solution of the linear quadratic problem of positive linear systems LQ+∞, i.e. The LQ-optimal closed-loop system remains positive and stable. Sufficient conditions are given that guarantee that the perturbation of a positive C0-semigroup by a negative operator generates a positive C0-semigroup. Our result is illustrated by an example.
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DOI: 10.1063/5.0194728
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