Bounding Errors Due to Switching Delays in Incrementally Stable Switched Systems (Extended Version)
For control engineers designing networked control systems, this work offers a method to bound errors from switching delays using the same stability assumption as state-space discretization, enabling a unified workflow.
The paper introduces a framework that provides an upper bound for errors caused by switching delays in incrementally stable switched systems, using approximate bisimulation. The framework is demonstrated on a boost DC-DC converter.
Time delays pose an important challenge in networked control systems, which are now ubiquitous. Focusing on switched systems, we introduce a framework that provides an upper bound for errors caused by switching delays. Our framework is based on approximate bisimulation, a notion that has been previously utilized mainly for symbolic (discrete) abstraction of state spaces. Notable in our framework is that, in deriving an approximate bisimulation and thus an error bound, we use a simple incremental stability assumption (namely δ-GUAS) that does not itself refer to time delays. That this is the same assumption used for state-space discretization enables a two-step workflow for control synthesis for switched systems, in which a single Lyapunov-type stability witness serves for two different purposes of state discretization and coping with time delays. We demonstrate the proposed framework with a boost DC-DC converter, a common example of switched systems.