Sensitivity to Cumulative Perturbations for a Class of Piecewise Constant Hybrid Systems
Provides a theoretical robustness guarantee for a class of hybrid systems relevant to scheduling and control.
The authors study the effect of external perturbations on a class of piecewise constant hybrid systems, including Max-Weight scheduling, and prove that the state deviation is bounded by a constant times the integral of the perturbation.
We consider a class of continuous-time hybrid dynamical systems that correspond to subgradient flows of a piecewise linear and convex potential function with finitely many pieces, and which include the fluid-level dynamics of the Max-Weight scheduling policy as a special case. We study the effect of an external disturbance/perturbation on the state trajectory, and establish that the magnitude of this effect can be bounded by a constant multiple of the integral of the perturbation.