Elementwise stablewise tracking with finite reachability time: Linear time-invariant continuous-time MIMO systems

Abstract

Three new qualitative control concepts are introduced and developed in the framework of general MIMO linear, time-invariant, continuous time systems to be controlled: natural trackability, elementwise and stablewise tracking, and natural tracking control. The study of these concepts opens new problems in control science, which are solved in the form of their necessary and sufficient conditions. Different physical natures and/or purposes of the system output variables, as well as their mutual independence, may require that each output be assigned a specific settling time and/or a reachability time. Such times compose corresponding vector times. The natural tracking control ensures elementwise output tracking which obeys a prespecified vector settling time and/or vector reachability time. A controller should use information only about the system output error and the realized control itself in order for the control to be natural tracking control. But the controller does not use any information about the system internal dynamics description, system state and external disturbances. The necessary and sufficient conditions are proved for the stability of systems that exhibit tracking. They permit possible independent and separate synthesis of a stabilizing control and of a tracking control. A natural tracking control synthesis and natural tracking controller design for a fourth-order MIMO system and simulation results illustrate and verify the new control theory avenues.