Insensitive H∞H∞ filter design for continuous-time systems with respect to filter coefficient variations

This paper is concerned with the problem of designing insensitive H∞H∞ filters for linear continuous-time systems. Coefficient sensitivity functions of transfer functions with respect to filter additive/multiplicative coefficient variations are defined, and the H∞H∞ norms of the sensitivity functions are used to measure the sensitivity of the transfer functions with respect to additive filter coefficient variations. In addition, in order to deal with the filter design problem for the multiplicative filter coefficient variation case, new measures based on the average of the sensitivity functions are also defined. Consequently, the insensitive H∞H∞ filter design problem is reduced to a multi-objective filter design problem, which minimizes the coefficient’s sensitivity and meets the prescribed H∞H∞ norm constraint simultaneously. First, a novel method for designing insensitive H∞H∞ filters subjected to additive filter coefficient variations is given in terms of the linear matrix inequality (LMI) optimization techniques. Furthermore, based on the new sensitivity measures, the obtained results are extended to the multiplicative coefficient variation case. In addition, an indirect method for solving the multiplicative variations is also proposed. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed method.