PD natural tracking control of an unstable chemical reaction

The concept of elementwise exponential tracking is defined as high quality tracking. Two related problems are solved: a) the necessary and sufficient condition for an object to be naturally trackable, and b) the synthesis of a PD natural tracking control so that its implementation guarantees elementwise exponential tracking. The theory is effectively applied to the synthesis of PD natural tracking control of an unstable chemical reaction, which will guarantee a prespecified elementwise exponential tracking.