Stablewise tracking with finite reachability time: linear time-invariant continuous-time MIMO systems

In the context of linear, time-invariant, continuous systems, the necessary and sufficient condition is proved for the existence of a control that can force the system to exhibit a requested tracking property without using any information about the mathematical description of the system internal dynamics and external disturbances. This property is the system trackability. A high-quality output error tracking algorithm expressing stablewise tracking with finite (prespecified) reachability time is then defined and proved. For natural trackable systems, a PD (proportional pulse derivative) control algorithm is synthesized to satisfy stablewise tracking with finite (given) reachability time without using a mathematical model of the system internal dynamics, its state, and the unmeasured, unknown time-varying disturbances. A MIMO (multiple-input multiple-output) system simulation illustrates the theory with prespecified stablewise tracking settling times.