Further Study On Pole Assignment For Linear Time-invariant System By Static Periodic Output

This paper is based on the algorithm of linear time-invariant discretesystems by static periodic output feedback. The purpose of this algorithm is tosearch in the controllable and observable discrete linear time-invariant systemsfor a series static periodic output feedback to take the poleassignment of closed loop systems, and reach the goal that the eige nvalues of thecharacteristic matrix of closed-loop systems are equal to the roots of thecharacteristic polynomial. It is a quite well periodic output feedback controlalgorithm, yet the precondition of the system applying this algorithm should becontrollable and observable and satisfy the condition that the product of theoutput matrix, inverse of characteristic matrix and input matrix unequal to zero.The main content here is to extend this algorithm to the sample-data system andcontinuous linear system, to see whether a periodic output feedback should befound to stabilize the according closed-loop systems. So we will discuss threeparts of content on the sample-data system following:1)when the previouscontinuous system is controllable and observable, how to choose propersample-data frequency to let new system also be controllable and observable.2)when the system operated is multi-input-multi-output, how to deal with thissystem.3)how to design the periodic output feedback controller. Then the nextwe will discuss two parts of content on the continuous linear system following:1)when the periodic output feedback is continuous, how to deal with the system.2) when the periodic output feedback is piecewise, how to deal with the system.Here we offer some result to the discussion of sample-data system, and putforward proposition on the continuous that output feedback will not stabilize thesystems in some conditions, and give the proof.