In this paper, we will present observer and output-based controller design methods for linear complementarity systems (LCS) employing a passivity approach. Given various inherent properties of LCS, such as the presence of state jumps, mode dynamics described by DAEs, and regions ("invariants") for certain modes being lower dimensional, several proposed observers and controllers for other classes of hybrid dynamical systems do not apply. We will provide sufficient conditions for the observer design for a LCS, which is effective also in the presence of state jumps. Using the certainty equivalence approach we obtain output-based controllers for which we will derive a separation principle.
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