An algebraic Riccati equation for the discrete-time periodic prediction problem

Abstract In this paper, the periodic problem is reformulated as a prediction problem relative to a suitable time-invariant system. This enables one to establish a one-to-one correspondence between the solutions of the Discrete-time Periodic Riccati Equation (DPRE) and the solutions of a suitable discrete-time and time-invariant Riccati equation. In particular, the constant solutions of this last equation are the periodic generators of the original periodic Riccati equation. This enables one to easily derive existence, uniqueness and convergence results for the DRPE from known results relative to the time-invariant case.

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