Robust elementwise exponential tracking control: IO linear systems

The system and control concepts of natural tractability, elementwise exponential tracking and natural tracking control are extended to time-invariant linear systems described by input-output n-th order vector differential equations with different control and output vector dimensions. The necessary and sufficient conditions are proved for a system to be natural trackable and for the natural tracking control synthesis to ensure a prespecified elementwise exponential tracking. The control synthesis is performed without the knowledge of the system internal dynamics. The natural trackability concept reflects an internal property of an object. A system possessing this property permits existence of a control that can force the output to elementwise exponentially converge to the desired output and which can be synthesized without using information about system dynamics and external disturbance. The tracking is guaranteed for any permitted pair of disturbance and desired output from prespecified functional families.