H ∞ filtering for Markovian jump delay systems with parameter uncertainties and limited communication capacity

Abstract

This study investigates the problem of robust H ∞ filter design for a class of Markovian jump time-varying delay systems with parameter uncertainties and limited communication capacity. The parameter uncertainties are norm bounded and the communication limitations include measurement quantisation, signal transmission delay and data packet dropout, which appear simultaneously in a networked control system framework. The authors aim to design mode-dependent H ∞ filter in the network environment so as to ensure the filtering error system is not only exponentially mean-square stable, but also satisfies a prescribed H ∞ -norm level for all admissible uncertainties and the limited communication capacity. The delay system method is used to cope with signal transmission delay and data packet dropout, and the sector bound approach is introduced to treat measurement quantisation. A stochastic Lyapunov-Krasovskii function is proposed to reflect the inherent mode-dependent state delays in the system itself, the network-induced signal transmission delay and data packet dropout, the free-weighting matrix technique and a set of strict linear matrix inequalities are utilised to derive novel conditions that guarantee the desired mode-dependent H ∞ filter can be constructed. A numerical example, a vertical take-off and landing helicopter system and a mass-spring system are presented to illustrate the effectiveness and usefulness of the main results obtained.