A linear programming framework for networked control system design∗

This paper considers stability and performance for a sampled data system with a distributed controller, time-varying delay, quantization, saturation, and external disturbances. We decompose the overall system into two subproblems. The first is a linear subsystem containing a distributed controller satisfying information sharing constraint between sensor and actuator. The second involves nonlinear error dynamics comprised of sampling, quantization, delay and saturation errors. We show how to construct an invariant set of the error dynamics using a linear program. Our method enables the design of distributed/localized controllers and delayed communication channels with linear programming, enhancing both implementation and design scalability. The use of l∞ signal/l1 operator norm appears essential to capture communication error and facilitate scalable computation. We also analyze the suboptimality gap and the feasibility condition of the proposed linear program.