Gain-scheduled filtering for time-varying discrete systems

This paper deals with the design of gain-scheduled filters, whose state-space realization depends on real-time parameters of plants. Similar to well-recognized advantages of gain-scheduled controllers in control theory, gain-scheduled filters are expected to provide enhanced performance in comparison with customary nonadjustable filters. Our construction technique is based on nonlinear fractional transformation (NFT) representations of systems that are a generalization of widely used linear fractional transformation (LFT) representations. Both generalized H₂ and H_∞ discrete-time filter design problems are investigated together with their extension to mixed designs. This study leads to new linear matrix inequality (LMI) formulations, which in turn provide an effective and reliable design tool. The proposed design technique is finally evaluated in the light of simulation examples.