Reachability and Controllability for Time - Invariant Control System with physical Applications

Abstract

The controller is an element which accepts the error in some form and decides the proper corrective action. The block diagrams is shorthand pictorial representation of control system of the cause-and-effect relationship between input and output of physical system or dynamic system is time invariant, is shifting the input of the time axis leads to an equivalent of shifting of the output along the time with no other changes. The aim of this research is study systems that the time invariant system and controllable. The controllability conditions are exactly the same in terms of the matrices for the discrete and continuous case. So we are justified in making multiple inputs, multiple outputs. Control system is a method for using any models of no solution for transfer functions and has extended tomultiple inputs, multiple outputs gained selection stability and process. It has been shown that the properties of zeros mean error and single input; single outputcase can be also achieved.Bounded variance amplification that was seen for themultiple inputs, multipleoutputs case. A design procedure is presented to achieved idealmultiple inputs, multiple outputscontrol case into more sensitivemodelingerror which are inherent in practical process. Ourapplication is the first solution follows from a general result on the global stabilization of controllable linear system with delay in the input by bounded control laws with a distributed term.