Anti-windup design for systems with input quantization

This paper presents a full-order anti-windup compensation strategy for LTI systems with input quantization. The anti-windup compensator functions by comparing the quantized and un-quantized control signal and attempting to ensure that the system´s behavior with quantization is close as possible to the ideal system behavior without quantization. The paper proposes an anti-windup compensator which can provide ultimate boundness stability conditions and also guarantee large-signal ℒ2 gain bounds. The problem is tackled by using the sector and boundness characteristics of the quantizer. The conditions for ultimate boundedness and large signal ℒ2 gain are formulated as a convex optimization problem which allows one to trade-off the size of the ball of ultimate boundedness with the ℒ2 performance objectives. The effectiveness of the proposed technique is shown through a simulation example.