International audienceIn 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

In this paper, the so-called Zen0 phenomenon is addressed for linear complementarity systems which are interconnections of linear systems and complementwity conditions. We present some sufficient conditions for absence of Zeno behavior. It is also shown that the zero state, which is the most obvious candidate for being a Zen0 state, cannot be a Zen0 state in certain cases.

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In this paper, the following notational conventions In this paper existence and uniqueness of solutions to linear complementarity systems (LCS) are considered. Complementarity systems are systems that are composed of differential equations, inequalities and switching logic. These systems can therefore be seen as a subclass of hybrid dynamical systems. The main result of this paper states that dissipativity of the underlying state space description of a LCS is a sufficient condition for existence of so-called initial solutions and guarantees uniqueness of the state trajectory. Applications of the results include electrical networks with diodes. will be in force. R denotes the real numbers, Et+ the nonnegative real numbers. For a positive integer IC, we denote the set (1,. . . IC} by k. Let a matrix M E Rkx' be given. For index sets I i, J C i, the submatrix M I J is defined as ( m t j ) i E I , j E J , where m;j denotes the entry of M in the i-th row and j-th column. If I = &, we also write M.J. Simila.rly, MI. is M I J with J = i. By Z we denote the identity matrix of any dimension.Finally, Cw(E3,E3) denotes all functions from R to E3 that are arbitrarily often differentiable.