Tube-Based Robust Smooth Transfer for Switched Systems

This note proposes a tube-based robust smooth transfer (TRST) control framework for a class of discrete-time switched systems under exogenous ℓ_∞ additive disturbances. TRST applies a set of smooth transfer (ST) controllers and stabilizing controllers alternately to guarantee the robust stability of system. Particularly, it ensures that the system state, control input, and their bumps during switches are all bounded within the respectively characterized tubes that depend on the disturbance amplitude. We derive control synthesis and tube-based analysis methods for generic asynchronously switched systems, which include the synchronous case as a special case. Furthermore, we propose a new criterion named absolute ST performance (ASTP) to evaluate the bump of the system induced by the disturbances, independent of system states. Finally, we employ an aero-engine control example to illustrate the application of TRST and show the advantage of ASTP over the commonly used state-dependent relative ST performance index.