Direct adaptive dynamic compensation for minimum phase systems with unknown relative degree

In the paper, some of the techniques of Marcel, I (1984) is adopted to develop lower order high-gain controllers that stabilize single-input single-output minimum phase systems with arbitrary known relative degree, correcting for the error encountered in Marcel, I (1984) when the relative degree exceeds four. Furthermore, a novel high-gain controller is developed for minimum phase systems when the relative degree is unknown-but-bounded. This construction makes uses of the Fibonacci series and a variation of root locus. A parameter-monotonic adaptation law is shown to guarantee state convergence to zero for a large class of high-gain stable closed-loop systems. Finally, this result is applied to the Fibonacci-based high-gain controllers. Thus, the main result of the paper is parameter-monotonic adaptive stabilization of single-input, single-output minimum phase systems with unknown-but-bounded relative degree.