# Stability of Riccati's Equation with Random Stationary Coefficients

Stability of Riccati's Equation with Random Stationary Coefficients 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 $(\bar P_t)$ of this Riccati equation. This solution is attracting, in the sense that if P t is another solution, then $P_t-\bar P_t$ onverges to 0 exponentially fast as t tends to +∞ , at a rate given by the smallest positive Lyapunov exponent of the associated Hamiltonian matrices. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

# Stability of Riccati's Equation with Random Stationary Coefficients

, Volume 40 (2) – Oct 1, 2074
22 pages

/lp/springer_journal/stability-of-riccati-s-equation-with-random-stationary-coefficients-WiVs7TqYwB
Publisher
Springer Journals
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s002459900119
Publisher site
See Article on Publisher Site

### Abstract

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 $(\bar P_t)$ of this Riccati equation. This solution is attracting, in the sense that if P t is another solution, then $P_t-\bar P_t$ onverges to 0 exponentially fast as t tends to +∞ , at a rate given by the smallest positive Lyapunov exponent of the associated Hamiltonian matrices.

### Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Oct 1, 2074

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Search Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly ### Organize Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. ### Access Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. DeepDyve ### Freelancer DeepDyve ### Pro Price FREE$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations