Robust filtering of discrete-time linear systems with parameter dependent Lyapunov functions. (English) Zbl 1022.93048

Geromel, J. C.; de Oliveira, M. C.; Bernussou, J.

SIAM J. Control Optimization 41, No. 3, 700-711 (2002).

This paper regards the robust filtering problem for linear time-invariant discrete-time systems using parameters dependent Lyapunov functions, when convex polytopic uncertainty is present in the dynamic, input, or output matrices. It bases on a new robust stability condition presenting a separation between the Lyapunov matrix and the matrices of the dynamic model. It is shown how to use such an approach to determine high performance \(H_2\) robust filters. Numerical examples illustrate the theoretical results.

Reviewer: Klaus Ehemann (Karlsruhe)

MSC:

93E11	Filtering in stochastic control theory
93C55	Discrete-time control/observation systems
93C05	Linear systems in control theory
93E15	Stochastic stability in control theory
93D30	Lyapunov and storage functions

Keywords:

linear systems; discrete-time systems; parameter uncertainty; robust filtering; parameter dependent Lyapunov functions; linear matrix inequalities; convex polytopic uncertainty; robust stability