A Smooth, High-Gain Adaptive Stabilizer for Linear Systems with Known Relative Degree

This paper considers the problem of adaptively stabilizing an unknown, continuous-time, minimum phase linear process with known, but arbitrary, relative degree n*. The controller is of dimension n* and is a one-parameter, high-gain design. The single gain parameter, k, is adjusted continuously as a function of process output, and is shown to adaptively stabilize any such process, provided that the process high frequency gain, g, lies in any known half-open interval (O,¿].