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This paper generalizes the LaSalle–Yoshizawa Theorem to switched nonsmooth systems. The Filippov and Krasovskii regularizations of a switched system are shown to be contained within the convex hull of the Filippov and Krasovskii regularizations of the subsystems, respectively. A common candidate Lyapunov function that has a negative semidefinite generalized time derivative along the trajectories of the subsystems is shown to be sufficient to establish LaSalle–Yoshizawa-like results for the switched system. Of independent interest, are the results on approximate continuity and Filippov regularization of set-valued maps, reduction of differential inclusions using Lipschitz continuous regular functions, and comparative remarks on different generalizations of the time derivative along the trajectories of a nonsmooth system. 

Functional electrical stimulation (FES) is commonly used for people with neurological conditions. As the muscle geometry changes (i.e., muscle lengthening/ shortening), the force induced by static electrode placement may also change. Experimental results indicate that muscle forces can be increased by spatially switching stimulation as the muscle geometry changes with joint angle. In this letter, an electric field is switched between multiple electrodes placed across the biceps brachii to track a desired trajectory. A switched systems approach is used to develop a position-based switching law, including a switched robust sliding mode controller that successfully tracks the desired angular trajectory about the elbow, despite changes in muscle geometry. Lyapunovbased methods for switched systems are used to prove global exponential tracking. Experimental results from nine able-bodied subjects are presented and the developed control system achieves an average position and velocity error of −0.21 ± 1.17 deg and −0.43 ± 5.38 deg/s, respectively, and, on average, reduces fatigue by 13.6%, as compared to traditional single-electrode methods, demonstrating the performance of the uncertain nonlinear switched control system.