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A new approach to functional observer design for linear time-delay systems

Designing functional observers for time-delay systems is an important practical research topic. However, the performance regulation of those observers and their robustness against the delays upper-bounds, have been fairly overlooked. In this brief, the problem of minimum order multi-functional observer design for Linear-Time-Invariant (LTI) systems with single state delay is revisited. Lyapunov Krasovskii approach is used to design the observer parameters in conjunction with the solution of some interconnected equations. A new methodology based on the descriptor transformation is proposed to construct a less conservative stability criterion compared with some other existing methods in designing delay-dependent functional observers. In addition, the exponential convergence of the observer with a specified convergence rate, is guaranteed. A numerical example shows the performance and the efficacy of the proposed design scheme.