Central suboptimal H∞ filter design for linear time-varying systems with state and measurement delays

This paper presents the central finite-dimensional H_∞ filters for linear systems with state and measurement delays, that are suboptimal for a given threshold g with respect to a modified Bolza-Meyer quadratic criterion including the attenuation control term with the opposite sign. The paper first presents the central suboptimal H_∞ filter for linear systems with state and measurement delays, which consists, in the general case, of an infinite set of differential equations. Then, the finite-dimensional central suboptimal H_∞ filter is designed in case of linear systems with commensurable state and measurement delays, which contains a finite number of equations for any fixed filtering horizon; however, this number still grows unboundedly as time goes to infinity. To overcome that difficulty, the alternative central suboptimal H_∞ filter is designed for linear systems with state and measurement delays, which is based on the alternative optimal H₂ filter from [39]. Numerical simulations are conducted to verify performance of the designed central suboptimal filters for linear systems with state and measurement delays against the central suboptimal H_∞ filter available for linear systems without delays.