Approximate Bisimulation for Switching Delays in Incrementally Stable Switched Systems

The recent rise of networked and cloud control poses time delays as a pressing challenge. Focusing on switched systems, we introduce an approximate bisimulation-based framework that provides an upper bound for errors caused by switching delays. We show that an incremental stability assumption can be exploited for establishing an approximate bisimulation and hence an error bound. This is the same assumption as in the existing framework for state-space discretization by Girard, Pola and Tabuada, and this fact helps to save a lot of efforts in the two-step control synthesis workflow that we propose. We present two examples for demonstration of our framework: a boost DC-DC converter (a common example of switched systems); and a nonlinear water tank.

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