Novel Observer‐Based Suboptimal Digital Tracker for a Class of Time‐Delay Singular Systems

This paper presents a novel suboptimal digital tracker for a class of time‐delay singular systems. First, some existing techniques are utilized to obtain an equivalent regular time‐delay system, which has a direct transmission term from input to output. The equivalent regular time‐delay system is important as it enables the optimal control theory to be conveniently combined with the digital redesign approach. The linear quadratic performance index, specified in the continuous‐time domain, can be discretized into an equivalent decoupled discrete‐time performance index using the newly developed extended delay‐free model. Additionally, although the extended delay‐free model is large, its advantage is the elimination of all delay terms (which included a new extended state vector), simplifying the proposed approach. As a result, the proposed approach can be applied to a class of time‐delay singular systems. An illustrative example demonstrates the effectiveness of the proposed design methodology.