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Uniform Convergence of Monotone Measure Differential Inclusions: with Application to the Control of Mechanical Systems with Unilateral Constraints

In this paper, we present theorems which give sufficient conditions for the uniform convergence of measure differential inclusions with certain maximal monotonicity properties. The framework of measure differential inclusions allows us to describe systems with state discontinuities. Moreover, we illustrate how these convergence results for measure differential inclusions can be exploited to solve tracking problems for certain classes of nonsmooth mechanical systems with friction and one-way clutches. Illustrative examples of convergent mechanical systems are discussed in detail.