Optimal guaranteed cost filtering for uncertain discrete-time linear systems

Abstract

This paper presents a result on the design of a steady‐state robust state estimator for a class of uncertain discrete‐time linear systems with normal bounded uncertainty. This result extends the steady state Kalman filter to the case in which the underlying system is uncertain. A procedure is given for the construction of a state estimator which minimizes a bound on the state error covariance. It is shown that this leads to a state estimator which is optimal with respect to a notion of quadratic guaranteed cost state estimation.

Robust Kalman filtering for discrete time-varying uncertain systems with multiplicative noises

“…Definition 1 [14], [26]: The filter (10) is said to be a quadratic filter associated with 6 k and P k if there exist symmetric positive-definite matrices 6 k and P k (0 k N) such that for all admissible uncertainty F k satisfying (2), the following inequality holds: ) and (27) are satisfied, where 8 k is given in (25).…”

A robust H/sub 2/ filtering approach and its application to equalizer design for communication systems

“…Therefore, we have (13) Inequality (13) is not easy to use when substituting filter parameters into . Therefore, we introduce another matrix such that (14) Thus, it is clear that Now, applying Schur complements [3] to (12) and (14), it is easy to establish the following corollary.…”

Robust H2 estimation and control

“…As compared to the results in [5,6], the result in Theorem 3.1 has the following advantages: (a) it achieves better filtering performance; (b) it does not require to search for the scaling parameters/" exphcitly as the optimization is convex in F; (c) it is more general as it encompasses the (state) estimation and deconvolution as special cases and (d) it does not impose any assumption on the system matrices such as the assumption that the matrix [ D He ] is of fi.fll row rank. Note that our result is optimal in the sense of [ 4 ], where a single block uncertainty appears in the system. Remark 3.3 It is worth noting that there have been many studies on systems with parameter uncertainty of polytopic type ( [ 15 -17] ) in recent years.…”