Local Capacity $H_{\infty }$ Control for Production Networks of Autonomous Work Systems With Time-Varying Delays

This paper considers the problem of local capacity H_∞ control for a class of production networks of autonomous work systems with time-varying delays in the capacity changes. The system under consideration is modeled in a discrete-time singular form. Attention is focused on the design of a controller gain for the local capacity adjustments which maintains the work-in-progress (WIP) in each work system in the vicinity of planned levels and guarantees the asymptotic stability of the system and reduces the effect of the disturbance input on the controlled output to a prescribed level. In terms of a matrix inequality, a sufficient condition for the solvability of this problem is presented using an appropriate Lyapunov function, which depends on the size of the delay and is solved by existing convex optimization techniques. When this matrix inequality is feasible, the controller gain can be found by using LMI Toolbox Matlab. Finally, numerical results are provided to demonstrate the proposed approach.