Central Suboptimal H ∞ Filter Design for Linear Time-Varying Systems with State or Measurement Delay

This paper presents the central finite-dimensional H∞ filters for linear systems with state and measurement delays, that are suboptimal for a given threshold γ 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.