This article studies the problem of prescribed-time global stabilization of a class of nonlinear systems, where the nonlinear functions are unknown but satisfy a linear growth condition. By using solutions to a class of parametric Lyapunov equations containing a time-varying parameter that goes to infinity as the time approaches the prescribed settling time, linear time-varying feedback is designed explicitly to solve the considered problem, with the help of a Lyapunov-like function. It is shown moreover that the control signal is uniformly bounded by a constant depending on the initial condition. Both linear state feedback and linear observer-based output feedback are considered. The effectiveness of the proposed approach is illustrated by a numerical example borrowed from the literature.

This study is concerned with stability analysis of non‐linear time‐varying systems by using Lyapunov function‐based approach. The classical Lyapunov stability theorems are generalised in the sense that the time‐derivative of the Lyapunov functions are allowed to be indefinite. The stability analysis is accomplished with the help of the scalar stable functions introduced in the author's previous study. Both asymptotic stability and input‐to‐state stability are considered. Particularly, for asymptotic stability, several concepts such as uniform and non‐uniform asymptotic stability, and uniform and non‐uniform exponential stability are studied. The effectiveness of the proposed theorems is illustrated by several numerical examples.

This technical note is concerned with output feedback consensus of both continuous-time and discrete-time multi-agent systems (MASs) characterized by high-order linear systems with directed communication topologies. Distributed reduced-order observer based protocols are established by only using the relative outputs and inputs of neighboring agents. It is shown that consensusability by the proposed output feedback protocols is equivalent to the consensusability by state feedback protocol. Under the condition that the open-loop dynamics of the MASs is not exponentially unstable, a truncated reduced-order observer based protocol utilizing only the relative outputs of neighboring agents is also established. A numerical example is given to illustrate the effectiveness of the proposed approaches.