Adaptive Control beyond Strictly Positive Real Systems

Abstract:

We study the extension of the class of linear time-invariant open-loop systems that may be transformed into SPR systems by introduction of observer dynamics. 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 restrictions of relative-degree-one conditions for the original input-output relationship. The result is illustrated with some examples of adaptive control applied to systems without SPR properties.