Nonfragile observerbased Hxe2x88x9e finitetime sliding mode control Abstract       H  xe2x88x9e     finitetime control for uncertain system with the unmeasurable state via the sliding mode control (SMC) approach is discussed in this article. Our attention is to design an appropriate finitetime SMC law to attenuate the influences of parametrical uncertainty and external disturbance. First, an appropriate nonfragile observerbased finitetime SMC law is designed such that the state trajectories can arrive at the specified sliding surface during the finitetime interval. Then, finitetime boundedness (FTBs) is well implemented by partitioning strategy and sufficient conditions are given to realize FTBs for the augment system with     H  xe2x88x9e     performance. Next, the controller gain and observer gain are obtained by solving the corresponding linear matrix inequalities (LMIs). Finally, a RLC series circuit shows the effectiveness of the proposed SMC approach.

Adaptive finitetime neural control of nonstrict feedback systems subject to output constraint, unknown control direction, and input nonlinearities Abstract   This paper addresses the finitetime controller design for a class of nonlinear systems in the nonstrict feedback form subject to unknown system dynamics and disturbances, arbitrary asymmetric timevarying output constraints, four types of input nonlinearities, and unknown control direction. Utilizing the barrier Lyapunov function (BLF) and backstepping technique, an adaptive finitetime controller has been proposed. The difficulties associating with nonstrict feedback systems have been handled using the variable separation approach. Furthermore, the unknown control direction problem has been tackled by using the Nussbaum gain function. A unified framework has been utilized for handling four types of input nonlinearities, including saturation, deadzone, backlash, and hysteresis. By applying intelligent approximators, not only the unknown functions been estimated, but also the explosion of complexity problem occurring in the backstepping technique has been avoided. To reduce the computational burden, only one adaptive law has been applied and the approximator functions are not involved in the control implementation. Under the designed controller, all closedloop signals remain semiglobally practically finitetime stable (SGPFS) and the tracking error converges to a small neighborhood of the origin in a finitetime. The effectiveness of the proposed controller has been demonstrated through a simulation example.