Infinite‐Dimensional Linear Systems: a Distributional Approach

We introduce the concept of a distributional resolvent linear system and solve the linear quadratic optimal control problem for this class of systems. The class of distributional resolvent linear systems includes all linear time-invariant systems that have been studied in the control literature. We show connections with integrated semigroups and distribution semigroups and we consider some examples of systems described by partial differential equations that could not be handled by the existing theory.

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