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

• Published in: Circuits, systems, and signal processing systems, and signal processing, 2009-04, Vol.28 (2), p.305-330
• Main Authors: Basin, Michael, Shi, Peng, Calderon-Alvarez, Dario, Wang, Jianfei
• Format: Article
• Language: English
• Subjects: Circuits and Systems; Control systems; Digital signal processors; Electrical Engineering; Electronics and Microelectronics; Engineering; Filters; Instrumentation; Low Power Digital Filter Design Techniques and Their Applications; Mathematics; Quadratic programming; Signal,Image and Speech Processing
• ISSN: 0278-081X; 1531-5878
• DOI: 10.1007/s00034-008-9077-0

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