An invariance principle for a class of ordinary differential equations with discontinuous right-hand side is developed. Based on this principle, asymptotic stability of one-degree-of-freedom mechanical oscillators with Coulomb friction is studied. The system is shown to be asymptotically stabilizable via a static feedback of the position, unlike those systems with no friction, whose stabilization requires a dynamic feedback when the position is the only available measurement. Along with this development, a velocity observer is proposed. Theoretical results of the paper are supported by some numerical simulations which, in addition, carry out a finite-time convergence of the controller and the observer proposed. [S0022-0434(00)00804-2]

This paper introduces a modern version of the classical Huygens’ experiment on synchronization of pendulum clocks. The version presented here consists of two monumental pendulum clocks—ad hoc designed and fabricated—which are coupled through a wooden structure. It is demonstrated that the coupled clocks exhibit ‘sympathetic’ motion, i.e. the pendula of the clocks oscillate in consonance and in the same direction. Interestingly, when the clocks are synchronized, the common oscillation frequency decreases, i.e. the clocks become slow and inaccurate. In order to rigorously explain these findings, a mathematical model for the coupled clocks is obtained by using well-established physical and mechanical laws and likewise, a theoretical analysis is conducted. Ultimately, the sympathy of two monumental pendulum clocks, interacting via a flexible coupling structure, is experimentally, numerically, and analytically demonstrated.

A procedure to design a global exponentially stable, second-order, sliding-mode observer for nDOF Lagrangian systems is presented. The observer converges to the system state in spite of the existence of bounded disturbances or parameter uncertainties affecting the system dynamics. The generation of sliding modes permits the identification of disturbances using the equivalent output injection which, under some circumstances, can also be used to identify the system parameters via a continuous version of the lastsquare method. The proposed methodology is illustrated with some numerical examples and experiments.

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