POLE ASSIGNMENT FOR LINEAR TIME-INVARIANT 2ND-ORDER SYSTEMS BY PERIODIC STATIC OUTPUT-FEEDBACK

It is well known that the poles of a linear time-invariant controllable observable system can be assigned arbitrarily by state feedback. When only the output is available, one usually resorts to dynamic output feedback in order to assign the poles of the system. Indeed, although some interesting results have been established on pole assignment by static time-invariant output feedback, the latter is not capable of giving the full array of possibilities available with dynamic output feedback or static state feedback. Another approach to the problem is to consider the potential of time-varying static output feedback. This type of feedback has been applied successfully in the context of decentralized systems. We present some results on pole assignment for second-order systems when allowing periodic static output feedback. For this class of systems, we offer a complete solution in the sense of giving conditions for the realizability of pole assignment by periodic output feedback.