This note investigates the problem of global output feedback stabilization for a class of nonlinear systems with unknown measurement sensitivity. A new design method, namely dual-domination approach, is proposed to explicitly construct a state observer as well as an output feedback control law, which globally asymptotically stabilizes the nonlinear systems. The novelty of this note owes to a distinct perspective in coping with unknown measurement sensitivity which has previously been a hurdle to solve the global output feedback stabilization problem of the nonlinear systems.

This paper aims to solve two intricate problems in nonlinear control: the singularity caused by driving the control to infinity at the prescribed time and the stabilization via adaptive event-triggered feedback for a class of uncertain nonlinear systems with asymmetric time-varying output constraints. The difficulty is how to dominate the implicit time in the system and the parameter error multiplied by an adaptive law without breaking the time-varying output constraint. To overcome the difficulty, we develop an event-triggered adaptive stabilizing controller comprising a time-varying scaling function and an exponential decay term, which is bounded on the whole-time interval and ensures that the states converge to the origin after entering a prescribed compact set within a prescribed finite time. Superior to the existing event-triggered schemes, the new triggered rule with a time-varying threshold guarantees that the designed controller is not only more robust against more serious uncertainties but also unifies the design in dealing with both constrained and unconstrained systems without constructing barrier functions associated with the output constraint. Finally, a practical simulation example is provided to illustrate and verify the effectiveness of the proposed approach.

The work has devised a novel fixed-time control scheme for a class of nonlinear systems with output constraints. Two distinctive features are incorporated into the gained results. One is that the upper bound of settling time for the closed-loop system can be estimated without dependence on system initial states, and hence, can be acquired arbitrarily small through tuning control design parameters. The other is that the output constraint can be handled by means of a barrier Lyapunov function (BLF). Via the BLF and the backstepping-like technique, a fixed-time controller, which can cope with a type of nonlinear systems concurrently with and without output constraints, is systematically built. The rigorous analysis on the strength of the Lyapunov theory is given to show that the investigated system under the proposed controller is fixed-time stable, and the violation of a preset output constraint is averted. The case studies of a series elastic actuator system are offered to substantiate the derived theoretical results.