Exponential Stabilization using Piecewise Constant Gain Adaptation
An adaptive stabilizer for a class of single-input-single-output (SISO) minimum phase systems with known sign is introduced. It extends the work of J.C. Willems and C.I. Byrnes (1984) but uses a threshold-based piecewise constant gain adaptation. This provides an exponential decaying state, and the set of thresholds which stabilize the terminal system exponentially is dense.