Passivity of nonlinear time-delay systems

This paper presents passivity-based control of nonlinear systems with retarded delays in the state. To this end, we first show that the standard passivity concept can naturally be generalized to time-delay systems, which readily implies that feedback interconnection (with or without communication delays) of passive time-delay systems is also passive. Then, we propose a storage functional for passivity analysis and further use it for stability analysis of controlledpassive time-delay systems. In particular, invoking an invariance principle for retarded functional differential equations, we show that a passive time-delay system can always be stabilized by a static output feedback controller under a delayed version of the zero-state detectability assumption.