Central energy-to-peak filter design for uncertain linear systems

This paper presents the central finite-dimensional energy-to-peak filter for linear systems that is optimal with respect to a modified Bolza-Meyer quadratic criterion including the first degree state-dependent term and the attenuation control term with the opposite sign. The obtained solution is based on reducing the original energy-to-peak filtering problem to the corresponding mean-module filtering problem, using the technique proposed in [1]. The paper first presents the central energy-to-peak filter for linear systems, based on the optimal mean-module filter from [2], assuming the standard filtering conditions of stabilizability, detectability, and noise orthonormality. Finally, to relax the standard conditions, the paper presents the generalized version of the designed energy-to-peak filter in the absence of the noise orthonormality. Numerical simulations are conducted to verify performance of the designed energy-to-peak filter for linear systems against the central suboptimal H
_∞
filter [3]. The simulation results show a definite advantage in the values of the noise-output energy-to-peak norm in favor of the designed filter.