Random evolutionary time-scale decomposition in robust control of jump linear systems

This paper addresses the issues of model simplification, decomposition, and design of robust reduced-order controllers in the context of piecewise-deterministic systems exhibiting distinguishable slow and fast modes in their form systems. The random jumps from one structure to another at random points in time are governed by a finite state Markov chain, and between two consecutive jumps the system admits a linear structure with open-loop slow and fast modes, where the dynamics are driven by not only a (state-feedback) control but also an unknown disturbance. Optimum slow and composite controllers are derived in the mathematical framework of H^∞ control (adapted to such hybrid systems), and their respective performances are evaluated. The theoretical results are then applied to a numerical example involving the robust control of a planar elbow manipulator with remotely driven links.