The authors present sufficient conditions for the design of strictly positive real (SPR), fixed-order dynamic compensators. The primary motivation for designing SPR compensators is for application to positive real (PR) plants. When an SPR compensator is connected to a PR plant in a negative feedback configuration, the closed loop is guaranteed stable for arbitrary plant variations as long as the plant remains PR. Equations that are a modified form of the optimal projection equations, with the separation principle not holding in either the full- or reduced-order case, are given. A solution to the design equations is shown to exist when the plant is PR (or just stable). Finally, the closed-loop system consisting of a PR plant and an SPR compensator is shown to be S-structured Lyapunov stable.
Proceedings of the 29th IEEE Conference on Decision and Control
Closed loop systems, Covariance matrix, Jacobian matrices, Negative feedback
Abdallah, Chaouki T.; M. Jacobus; M. Jamshidi; Peter Dorato; and D. Bernstein. "Design of strictly positive real, fixed-order dynamic compensators." Proceedings of the 29th IEEE Conference on Decision and Control (1990): 3492-3496. doi:10.1109/CDC.1990.203452.