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Abstract-This paper considers the stabilization and synchronization of Chua's oscillators via an impulsive control with time-varying impulse intervals. Some less conservative conditions were derived in the sense that the Lyapunov function is only required to be nonincreasing along a subsequence of the switchings.

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An equivalent linear matrix inequality LMI representation of bounded real lemma BRL for linear continuous-time systems is introduced. As to LTI system including polytopic-type uncertainties, by using a parameter-dependent Lyapunov function, there are several LMIs-based formulations for the analysis and synthesis of H∞ performance. All of these representations only provide us with different sufficient conditions. Compared with previous methods, this new representation proposed here provides us the possibility to obtain better results. Finally, some numerical examples are illustrated to show the effectiveness of proposed method.

SUMMARYThe full-state stabilization scheme is proposed for the control of an underactuated surface vessel with unknown modeling parameters. By knowing only the upper/lower bounds of model parameters, the designed controller is the first one able to globally uniformly asymptotically stabilize all the states of the vessel to zero. The virtual surge velocity control law is first derived, which makes the Lyapunov function at the kinematic level non-increasing, irrelevant to the yaw velocity, leaving a freedom for choosing the virtual yaw velocity control law to stabilize the other state variables. After finishing the design of virtual velocity law, the back-stepping approach and the Lyapunov redesign technique are combined to obtain the actual force/torque control law despite parameter uncertainties. Simulation examples are given to illustrate the effectiveness of the proposed control law, showing that all the states and the control inputs are globally uniformly asymptotically convergent to zero under parameter uncertainties and are globally bounded under unknown external bounded disturbances.