An LMI approach to the H/sub /spl infin// filter design for uncertain systems with distributed delays

This paper investigates the problem of robust H/sub /spl infin// filter design for linear distributed delay systems with norm-bounded time-varying parameter uncertainties. The distributed delays are assumed to appear in both the state and measurement equations. The problem we address is the design of a filter, such that for all admissible uncertainties, the resulting error system is asymptotically stable and satisfies a prescribed H/sub /spl infin// performance level. A sufficient condition is obtained to guarantee the existence of desired H/sub /spl infin// filters, which can be constructed by solving certain linear matrix inequalities. The effectiveness of the proposed design method is demonstrated by a numerical example.

I. Introduction

Time delays are frequently encountered in many practical engineering systems, such as communication, electronics, hydraulic, and chemical systems. It has been shown that the presence of a time delay in a dynamical system is often a primary source of instability and performance degradation [6]. This has motivated the study of time-delay systems, and a great number of results on the control and filtering for control systems with time delays have been reported in the literature; see, e.g., [3] and [6]–[8], and the references therein. It is noted that these results are derived for systems with discrete delays. When the number of summands in a system equation is increased and the differences between neighboring argument values are decreased, systems with distributed delays will arise. Therefore, distributed delay systems have received much attention in the past years. Distributed delay occurs in the modeling of feeding systems and combustion chambers in a liquid monopropellant rocket motor with pressure feeding [2], [5]. Some stability and robust control results for such systems can be found in [9], and the references therein.