Mixed H₂/H_∞ filtering design in multirate transmultiplexer systems: LMI approach

A mixed H₂/H_∞ filter design is proposed for multirate transmultiplexer systems with dispersive channel and additive noise. First, a multirate state-space representation is introduced for the transmultiplexer with the consideration of channel dispersion. Then, the problem of signal reconstruction can be regarded as a state estimation problem. In order to design an efficient separating filterbank for a transmultiplexer system with uncertain input signal and additive noise, the H_∞ filter is employed for robust signal reconstruction. The H₂ filter design is considered to be a suboptimal approach to achieve the optimal signal reconstruction in transmultiplexer system under unitary noise power. Finally, a mixed H₂/H_∞ filter is proposed to achieve a better signal reconstruction performance in transmultiplexer systems. These design problems can be transformed to solving the eigenvalue problems (EVP) under some linear matrix inequality (LMI) constraint. The LMI Matlab toolbox can be applied to efficiently solve the EVP by convex optimization technique