A frequency domain analysis of the second-order sliding-mode algorithms, particularly of the twisting algorithm is carried out in the frequency domain with the use of the describing function method and Tsypkin's approach. It is shown that in the presence of an actuator, the transient process may converge to a periodic motion. Parameters of this periodic motion are analyzed. A comparison of the periodic solutions in the systems with higher order sliding-mode controllers and the oscillations that

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... occur in classical sliding-mode systems with actuators is done. Index Terms-Chattering, relay control, sliding-mode (SM) , variable structure systems. Abstract-This note revisits the problem of stability analysis for linear systems under state constraints. New and less conservative sufficient conditions are identified under which such systems are globally asymptotically stable. Based on these sufficient conditions, iterative linear matrix inequality (LMI) algorithms are proposed for testing global asymptotic stability of the system. In addition, these iterative LMI algorithms can be adapted for the design of globally stabilizing state feedback gains.