Finite-time H∞ control for a class of nonlinear system with time-varying delay

This paper is concerned with the finite-time H∞H∞ control for a class of nonlinear system with time-varying delay, which can be represented by Takagi–Sugeno (T–S) fuzzy system. First, a new integral inequality, which is less conservative than other existing ones, is established by introducing some free fuzzy weighting matrices. Based on a new fuzzy Lyapunov–Krasovskii function, delay-dependent finite-time boundedness (FTB) criterion and H∞H∞ finite-time boundedness (H∞H∞ FTB) criterion are derived for the open-loop fuzzy time-delay system. Then, some delay-dependent finite-time stabilization conditions are given by designing a memory state feedback controller, which is based on the so-called parallel distributed compensation (PDC) scheme. Finally, an example is provided to illustrate the validity of the proposed design approach.