Stability of Riccati's Equation with Random Stationary Coefficients

Journal Article · Wed Sep 15 00:00:00 EDT 1999 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S002459900119· OSTI ID:21064283

Fakhfakh, S ^[1]

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1. Laboratoire de Probabilites, Departement de Mathematiques Faculte des Sciences de Sfax, CP 3038 Sfax (Tunisia)

The purpose of this paper is to study under weak conditions of stabilizability and detectability, the asymptotic behavior of the matrix Riccati equation which arises in stochastic control and filtering with random stationary coefficients. We prove the existence of a stationary solution (P-bar{sub t}) of this Riccati equation. This solution is attracting, in the sense that if P{sub t} is another solution, then P{sub t}-P-bar{sub t} converges to 0 exponentially fast as t tends to +{infinity} , at a rate given by the smallest positive Lyapunov exponent of the associated Hamiltonian matrices.

• OSTI ID: 21064283
• Journal Information: Applied Mathematics and Optimization, Vol. 40, Issue 2; Other Information: DOI: 10.1007/s002459900119; Copyright (c) 1999 Springer-Verlag New York Inc.; Article Copyright (c) Inc. 1999 Springer-Verlag New York; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ASYMPTOTIC SOLUTIONS
CONTROL THEORY
HAMILTONIANS
LYAPUNOV METHOD
MATRICES
RANDOMNESS
RICCATI EQUATION
STABILITY
STOCHASTIC PROCESSES