Robust PID Multi-Line Stability Conditions for FNFR Models

The objective of this paper is to introduce a new stability condition, a “multi-line” stability condition and to propose robust PID controller design methods based upon it for non-parametric models represented by a finite number of frequency responses (FNFR models). The “multi-line” stability condition is introduced for reducing the conservativeness of the “single-line” stability condition proposed for closed-loop stability in previous works. Then, new robust PID controller design problems based upon the “multi-line” stability condition are formulated as convex optimization problems.