Finite-time control for uncertain systems with nonlinear perturbations

This study investigates the problem of finite-time control for uncertain systems with nonlinear perturbations. The aim is to design the state-feedback and output-feedback controller which ensure finite-time boundedness and with a desired H ∞ $H_{\infty}$ performance index υ. Specifically, first, we divide the time-varying delay into non-uniformly subintervals and decompose the corresponding integral intervals to estimate the bounds of integral terms exactly. Second, the conditions obtained in this paper are formulated in terms of linear matrix inequalities (LMIs), which can be efficiently solved via standard numerical software. Finally, numerical examples are presented to demonstrate the effectiveness and advantages of the theoretical results.