Unified Output Feedback Design and Loop Transfer Recovery

Abstract

Abastract This paper presents, for the first time, a systematic, general, and simple design procedure for a dynamic output feedback (DOF) compensator whose internal state z(t) converges to a linear transformation of open loop system states Tx(t). This procedure is valid for all observable systems {A,B,C} with more outputs than inputs, and is valid for arbitrary (but stable) compensator poles. The unique property z(t)→Tx(t) guarantees uniquely the following four significant advantages and developments. 1). this compensator implements a perfectly equivalent yet more powerful static output feedback (SOF), which is also equivalent of a constrained state feedback (SF). 2). this compensator guarantees exact and finite gain LTR for this constrained SF, and therefore significantly reduces the restrictions of the existing result of exact or finite gain LTR (restrictions of minimum-phase and rank(CB)=rank(B) are omitted). Therefore, our constrained SF is more reasonably deigned than the normally formulated SF which is designed independent of LTR observer implementation. 3). this compensator perfectly unifies SOF and arbitrary SF with exact LTR observer implementation, as its two extreme structures. 4). this compensator guarantees the critical separation principle of the corresponding closed loop system