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The observer‐based linear quadratic sub‐optimal digital tracker for analog systems with input and state delays

This paper presents a new observer‐based sub‐optimal digital tracker for the continuous‐time system with input and state time delays. We directly convert the continuous‐time input‐state delayed system into an equivalent discrete‐time input‐state delayed model and its extended discrete‐time delay‐free model. In addition, we directly discretize the linear quadratic performance index specified in the continuous‐time domain into an equivalent decoupled discrete‐time performance index using the newly developed extended delay‐free model. As a consequence, the well‐developed discrete‐time optimal control theory for discrete‐time delay‐free system can be applied to determine the optimal digital tracker for the continuous‐time input‐state delayed system. When the states of the continuous‐time input‐state delayed system are not available for measurements, we develop a sub‐optimal digital observer for the original continuous‐time input‐state delayed system using the state‐matching digital redesign technique and the digital‐to‐analog model conversion technique. As a result, the proposed observer‐based linear quadratic digital tracker is able to make the output of the digitally controlled continuous‐time input‐state delayed system sub‐optimally track the desired reference signals. An illustrative example is presented to demonstrate the effectiveness of the proposed design methodology. Copyright © 2003 John Wiley & Sons, Ltd.