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We solve a linear quadratic optimal control problem for sampled-data systemswith stochastic delays. The delays are stochastically determined by the lastfew delays. The proposed optimal controller can be efficiently computed byiteratively solving a Riccati difference equation, provided that adiscrete-time Markov jump system equivalent to the sampled-data system isstochastic stabilizable and detectable. Sufficient conditions for these notionsare provided in the form of linear matrix inequalities, from which stabilizingcontrollers and state observers can be constructed.

LQ-optimal Sample-data Control under Stochastic Delays: Gridding Approach for Stabilizability and Detectability