A max-plus primal space fundamental solution for a class of differential Riccati equations

A class of differential Riccati equations (DREs) is considered for which the evolution of any solution can be identified with the propagation of a value function of a corresponding optimal control problem arising in $${\mathscr {L}_2}$$L2-gain analysis. By exploiting the semigroup properties inherited from the attendant dynamic programming principle, a max-plus primal space fundamental solution semigroup of max-plus linear max-plus integral operators is developed that encapsulates all such value function propagations. Using this semigroup, a one-parameter fundamental solution semigroup of matrices is constructed for the aforementioned class of DREs. It is demonstrated that this semigroup can be used to compute particular solutions of these DREs, and to characterize finite escape times (should they exist) in a simple way.

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