Observer-Based Solution to the Strictly Positive Real Problem

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 using cascade or cascade and feedback controllers. This overcomes the old conditions of minimum phase and relative degree one. The result is illustrated with some examples.