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

Abstract

This paper presents central finite-dimensional H ? filters for linear systems with state or measurement delay that are suboptimal for a given threshold ? with respect to a modified Bolza---Meyer quadratic criterion including an attenuation control term with opposite sign. In contrast to the results previously obtained for linear time-delay systems, the paper reduces the original H ? filtering problems to H 2 (optimal mean-square) filtering problems, using the technique proposed in Doyle et al. (IEEE Trans. Automat. Contr. AC-34:831---847, 1989). The paper first presents a central suboptimal H ? filter for linear systems with state delay, based on the optimal H 2 filter from Basin et al. (IEEE Trans. Automat. Contr. AC-50:684---690, 2005), which contains a finite number of filtering equations for any fixed filtering horizon, but this number grows unboundedly as time goes to infinity. To overcome that difficulty, an alternative central suboptimal H ? filter is designed for linear systems with state delay, which is based on the alternative optimal H 2 filter from Basin et al. (Int. J. Adapt. Control Signal Process. 20(10):509---517, 2006). Then, the paper presents a central suboptimal H ? filter for linear systems with measurement delay, based on the optimal H 2 filter from Basin and Martinez-Zuniga (Int. J. Robust Nonlinear Control 14(8):685---696, 2004). Numerical simulations are conducted to verify the performance of the designed three central suboptimal filters for linear systems with state or measurement delay against the central suboptimal H ? filter available for linear systems without delays.