Summary In this article, the global stabilization of a class of underactuated mechanical systems of two degrees of freedom (DoF) is addressed, despite the presence of Lipschitz disturbances and/or uncertainties and uncertain control coefficient in the model. Using two second‐order continuous sliding modes algorithms, the control task is performed, reaching finite‐time convergence in one part of the dynamics and generating a continuous control signal. The efficacy of the proposed controllers is illustrated via simulations for the reaction wheel pendulum (RWP) and the translational oscillator with rotational actuator (TORA) systems, and by means of experiments on the RWP system, comparing the presented algorithms with a linearizing controller.

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The fourth-order model of the reaction wheel pendulum is considered and a fourth-order discontinuous integral algorithm is used for stabilization and tracking of the system, using a continuous control signal. The states reach the origin or a reference signal in finite-time, even in presence of uncertain control coefficient and a kind of matched and unmatched uncertainties/disturbances. A homogeneous Lyapunov function is designed to ensure local finite-time stability of the system, which can be used for designing the controller gains. Simulations and experimental results illustrate the performance and advantages of the presented algorithm. K E Y W O R D S finite-time convergence, higher-order sliding-mode control, nonlinear control, tracking control, wheel pendulum Abbreviations: 3-DIA, third order discontinuous integral algorithm; 4-DIA, fourth order discontinuous integral algorithm; RWP, reaction wheel pendulum.

Two recent results on earthquake control are summarized. A simplified model of an earthquake phenomenon is addressed by means of a cascade system of a 1D wave equation, representing the fault slip and wave propagation, and a 1D diffusion equation, representing the actuator dynamics as a diffusion process. In order to avoid a fast slip (earthquakelike behaviour), the control is designed to follow a slow reference. The control strategies are presented separately for both Partial Differential Equations (PDEs). For the wave PDE, a homogeneous boundary tracking control is developed to achieve exponential Input to State Stability (eISS) of the error closedloop dynamics. For the diffusion PDE, Proportional Integral (PI) and a discontinuous integral term are coupled to exponentially stabilize the error origin despite model uncertainties and perturbations. Simulations are additionally conducted to support the robustness and stability properties of the proposed control algorithms, by separately, obtaining critical remarks that will lead to the design of the single control for the cascade system in a future stage.