Strictly positive real systems based on reduced-order observers

We study the extension of the class of linear time-invariant open-loop systems that may be transformed into SPR systems introducing a reduced-order observer. It is shown that for open-loop stable systems a cascaded observer achieves the result. For open-loop unstable systems 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.