ROBUST H{sub}∞ OBSERVERS FOR UNCERTAIN TIME-DELAY SYSTEMS: (I) THE CONTINUOUS-TIME CASE

摘要

This note deals with the problem of H{sub}∞ observer design for a class of uncertain linear systems with delayed state and parameter uncertainties. This problem aims at designing the linear state observers such that, for all admissible parameteruncertainties, the observation process remains robustly stable and the transfer function from exogenous disturbances to error state outputs meets the prespecified H{sub}∞ norm upper bound constraint, independently of the time-delay. The time-delay isassumed to be small but unknown, and the parameter uncertainties are allowed to be norm-bounded and appear in all the matrices of the state-space model. An effective matrix inequality methodology is developed to solve the proposed problem. We derive theconditions for the existence of the desired robust H{sub}∞ observers, and then characterize the analytical expression of these observers. A numerical example demonstrates the validity and applicability of the present approach.