High-gain natural tracking control of time-invariant systems described by IO differential equations

The concept of finite-time and infinite-time system trackability is introduced. A feature which must be present in a system in order that it may be able to exhibit tracking is found. The necessary and sufficient condition is proved for both finite-time and infinite-time trackability for time-invariant linear systems described by input-output differential equations. A control that can be synthesized and implemented without using information about the system internal dynamics and which ensures a tracking property is called natural tracking control. Sufficient conditions are proved for synthesis of high-gain natural tracking control.