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. GLOBAL OUTPUT-FEEDBACK STABILIZATION 805 system output, and therefore, the feedback stabilization is more difficult to solve. Furthermore, when the nonlinear systems also have parameter unknowns, which may exist in the control coefficients and/or the nonlinearities of the systems, the corresponding feedback stabilization would pose a greater challenge to the existing theory of stabilization and probably motivates the new patterns of control design. With the development on the topic, approaches such as homogeneous domination and certainty equivalence principle, and some compensator schemes have been proposed (see e.g., [12,13,16,25,27,30,32]), and the main progress so far focuses on the following four aspects:(i) The nonlinear system is of high-order or not. The high-order nonlinear system and the nonhigh-order one were investigated in [13,17,20,23,24,27,31] and [10-12, 14-16, 18, 19, 21, 22, 25, 26, 28-30, 32], respectively. The former has uncontrollable modes in its linearized system, and hence, its nonlinearities are more inherent than those of the latter. (ii) The system growth is higher-order and/or lower-order with respect to unmeasured states.The cases of higher-order and lower-order system growths were considered in [10-12, 14-16, 18, 20-22, 25, 26, 29, 30, 32] and [17,24,31], respectively, both indicating serious immeasurableness in the systems. The former consists of the homogeneous system growth [16,20] and the linear system growth [10-12, 14, 15, 18, 21, 22, 25, 26, 29, 30, 32]. The more general case that higher-order system growth and lower-order one simultaneously exist in a system was considered in [23,27,28]. (iii) The system growth rate is precisely known or unknown, and it is a constant, a polynomial of output or a function of output. The system growth rates in [10,13,16,17,19,20,23,26,28], [12,27] and [14,24] are known ...
