Mixed H2/H∞ Filtering for Continuous-Time Polytopic Systems: A Parameter-Dependent Approach

Abstract

The problem of mixed H 2 /H ∞ filtering is investigated for continuous-time polytopic systems. Given a stable system whose parameters reside in a polytope and can be measured online, attention is focused on the design of parameter-dependent filters such that the filtering error system is asymptotically stable and has guaranteed H 2 and H ∞ performances with respect to different input signals. By introducing multiple Lyapunov functions, the parameter-dependent approach developed in this paper is able to yield much less conservative filters than the existing results. A numerical example is provided to show the effectiveness and reduced conservatism of the proposed theory.

A Generalized Parameter-Dependent Approach to Robust H ∞ Filtering of Stochastic Systems

“…First (18) implies T + T T −Q 3λ > 0; then we know that T is nonsingular due tõ Q 3λ > 0. Thus, one can always find square and nonsingular matrix functions V 3 and V 4 satisfying (17). Now introduce the matrix functions φ,φ as defined in (15) and …”

“…Solving the problem of robust filtering via parameter-dependent Lyapunov functions is an advanced research topic, whose aim is to reduce the overdesign in the quadratic framework. Nowadays, there are several linear matrix inequality (LMI) conditions for robust filter design of complex systems based on parameter-dependent Lyapunov functions, including uncertain linear systems [2,15,17], time-delay systems [34], and stochastic systems [29,33]. By utilizing the parameter-dependent approach, these results are generally less conservative than those in the quadratic framework, most of which have either been proved theoretically or illustrated through numerical examples.…”

Robust Adaptive Filter for Small Satellite Attitude Estimation Based on Magnetometer and Gyro

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Improved H ∞ Filtering for Systems with a Time-Varying Delay

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