Analysis and design of feedback systems with gain and time constant variations

The design of a feedback control system containing an element with proportional variation of gain and time constant is a common problem encountered by control engineers in practice. The problem includes the stabilization of a system, which is open-loop unstable when both the gain and the time constant of the element are negative. This paper presents a method for analyzing the transient response of systems containing the aforementioned element, and designing the systems to meet transient specifications.