Filtering Design for Multirate Sampled-Data Systems

The problem of <inline-formula> <tex-math notation="LaTeX">${\mathcal {H}}_{\infty }$ </tex-math></inline-formula> filtering to estimate the unmeasurable states is investigated in this paper and the most general multirate measurements condition is taken into account. The main result of this paper is to give a method to design a filter, which can guarantee the stability of the resultant filtering error system with <inline-formula> <tex-math notation="LaTeX">${\mathcal {H}}_{\infty }$ </tex-math></inline-formula> performance. For a given system with multirate measurements, this paper first provides a method to convert this multirate design problem into an equivalent single-rate design problem. Then, it can be proved that the design approach of a required filter based on a linear matrix inequality is a sufficient and necessary condition. Lastly, two examples are utilized to demonstrate that this design approach is effective and applicable to estimate the unmeasurable states for the given system with multirate measurements.

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