ABSTRACT
The linear tracking control (LITC) synthesis in the complex domain demands the use of the system full transfer function matrix F (s) (rather than of the system transfer function matrix G(s) that is insu¢ cient). This illustrates the theoretical and practical importance and the wide engineering applications of the system full transfer function matrix F (s): Various new Lyapunov tracking control (LTC) algorithms are established
herein in order to guarantee the corresponding tracking properties. Scalar Lyapunov functions are the basis for some of them, and the vector Lyapunov function is the background for others. When they are linked with the tracking algorithm, then the problem, which is caused by the annulment of Lyapunov function gradient, does not exist. Beside, the use of the subsidiary error vector , instead of the real error vector ", permits us to avoid the problem of control discontinuity and chattering. By analyzing information that nature uses to generate control we introduced
the concept of the Natural Tracking Control (NTC). NTC algorithms are associated with the tracking properties. The necessary
and su¢ cient conditions are proved for NTC synthesis to guarantee the chosen tracking property.
