H∞ filtering for sampled-data systems

This paper is concerned with H_∞ filtering for linear sampled-data systems. The system is usually modelled as a continuous-time system, while in practical situations the measurement outputs are taken at discrete instants. Such measurement outputs can be represented as delayed signals. First it is shown that the error system which stems from an original linear system and a sampled-data filter becomes a system with time-varying delay. Sufficient conditions for the error system to achieve the asymptotic stability with H_∞ disturbance attenuation are given in terms of linear matrix inequalities(LMIs). We derive such conditions via output delay system approach under the assumption that sampling-time is not greater than some prescribed number. Based on such conditions, we propose a few H_∞ sampled-data filter design methods for a linear system. Numerical examples are given to illustrate our H_∞ sampled-data filtering.