Global output‐feedback stabilization for high‐order nonlinear systems with unknown growth rate

This paper considers the global stabilization via time‐varying output‐feedback for a class of high‐order uncertain nonlinear systems with rather weak assumptions. Essentially different from the existing literature, the systems under investigation simultaneously have more serious nonlinearities, unknowns, immeasurableness, and time‐variations, which are indicated from the unknown time‐varying control coefficients and the higher‐order and lower‐order unmeasured states dependent growth with the rate of unknown function of time and output. Recognizing that adaptive technique is quite hard to apply, a time‐varying design scheme is proposed by combining time‐varying approach, certainty equivalence principle and homogeneous domination approach. One key point in the design scheme is the selection of the design functions of time, in order to compensate/capture the serious unknowns and serious time‐variations, and another one is the design of a time‐varying observer to rebuild the unmeasured system states. With the appropriate choice of the involved design functions, the designed controller makes all the signals of the closed‐loop system globally bounded and ultimately converge to zero. Copyright © 2016 John Wiley & Sons, Ltd.