Abstract
The object of the study is a class of switched nonlinear systems with uncontrollable and unobservable linearized models, such as those arising in aerospace, power electronic, and robotics applications, where only output information is available for feedback. The problem to be solved is the global finite-time control for a class of high-order switched nonlinear time-delay systems via output feedback under arbitrary switching, where the powers and nonlinearities depend on the switching signal. First, using the adding-a-power-integrator technique, a homogeneous output-feedback controller is developed for the nominal part of the switched nonlinear system. Then, the constructed observer and controller are rescaled via the homogeneous domination approach and a common coordinate transformation is introduced to eliminate the dependence of the transformed dynamics on the switching signal. Together with an appropriately constructed Lyapunov-Krasovskii functional, this approach guarantees that the closed-loop switched high-order nonlinear system with time-varying delay is globally finite-time stable. The proposed framework simultaneously addresses switching-dependent nonlinearities, time-varying delays and output-feedback-based finite-time stabilization within a unified design, unlike existing results that handle these difficulties only separately. A numerical example demonstrates the effectiveness of the proposed controller and observer: the system states converge to zero in finite time, the control input remains bounded and the observer accurately reconstructs the unmeasured state despite the time-varying delays, confirming the practical applicability of the method to switched systems with output-only sensing and communication delays