On the matrix Riccati equation for a singularly perturbed linear discrete control system

Abstract A difference approximation to a singularly perturbed linear, time-varying, continuous-time control system is presented, and is called a singularly perturbed linear discrete-time control system. Under several assumptions, it is shown that the Riccati equation for the reduced system, in the sense of singular perturbation, agrees with that for the associated subsystem of the full (non-reduced) system when a small parameter in the equation is set zero. On the basis of this result, it is also shown that the optimal controls and the corresponding trajectories for the two systems are consistent with each other when a small parameter for the full system is set zero.

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