Using an observer to transform linear systems into strictly positive real systems

In this note, we study the extension of the class of linear time invariant plants that may be transformed into SPR systems introducing an observer. It is shown that for open loop stable systems a cascaded observer achieves the result. For open loop unstable systems an observer-based feedback is required to succeed. In general any stabilizable and observable system may be transformed into an SPR system defining a new output based on the observer state. This overcomes the old conditions of minimum phase and relative degree one for the case of keeping the original output. The result is illustrated with some examples. Index Terms--Kalman-Yakubovich-Popov (KYP) lemma, Lyapunov functions, observers, passivity, strictly positive realness (SPR), strictly positive realness (SPR) systems.