Riccati differential equation in optimal filtering of periodic non-stabilizable systems |
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Authors: | CARLOS E DE SOUZA |
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Affiliation: | Department of Electrical and Computer Engineering , University of Newcastle , New South Wales , 2308 , Australia |
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Abstract: | This paper discusses the periodic solutions of the matrix Riccati differential equation in the optimal filtering of periodic systems. Special emphasis is given to non-stabilizable systems and the question addressed is the existence and uniqueness of a steady-state periodic non-negative definite solution of the periodic Riccati differential equation which gives rise to an asymptotically stable steady-state filter. The results presented show that the stabilizability is not a necessary condition for the existence of such a periodic solution. The convergence of the general solution of the periodic Riccati differential equation to a periodic equilibrium solution is also investigated. The results are extensions of existing time-invariant systems results to the case of periodic systems |
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