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This technical note deals with a modified algebraic Riccati equation (MARE) and its corresponding inequality and difference equation, which arise in modified optimal control and filtering problems and are introduced into the cooperative control problems recently. The stabilizing property of the solution to MARE is presented. Then, the uniqueness is proved for the almost stabilizing and positive semi-definite...
In this paper we develop a reduction technique for the generalised Riccati difference equation arising in optimal control and optimal filtering. This technique relies on a decomposition method for the generalised Riccati difference equation that isolates its nilpotent part, which becomes constant in a number of iteration steps equal to the nilpotency index of the closed-loop, from another part that...
We study certain difference equations arising in the stability analysis of Kalman filtering for a class of linear, discrete-time, possibly non-detectable systems with incorrect noise information. We obtain bounds for the solutions of these equations and the Riccati difference equation associated with the Kalman filter, under the assumption that the Riccati solution is bounded above and an assumption...
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