A polyhedral approach to the stability analysis and feedback stabilization of networked control systems

In this note, the stability analysis and control design of Networked Control Systems (NCS) with bounded transmission delays, constant and unknown or time varying, is investigated using polyhedral Lyapunov functions. First, conditions guaranteeing stability are formulated for the equivalent augmented discrete-time system with structured uncertainties. Then, algebraic conditions leading to the computation of a linear state feedback controller for a NCS with bounded time varying delays are established. Both the stability analysis and synthesis problem are reduced to linear programming methods, a welcome consequence stemming from the choice of polyhedral Lyapunov functions.