Frequency domain performance bounds for uncertain positive real plants controlled by strictly positive real compensators

An important part of feedback control involves analyzing uncertain systems for robust stability and performance. Many robustness theories consider only stability issues and ignore performance. Most of the performance robustness results that do exist will not always yield finite performance bounds for the case of closed-loop systems consisting of uncertain positive real plants controlled by strictly positive real compensators. These results are obviously conservative since this class of systems is unconditionally stable. This paper uses majorant analysis to develop tests that yield finite performance bounds for the above case. The results are specialized to the case of static, decentralized colocated rate feedback and dynamic colocated rate feedback.