Observer-Based Control for Piecewise-Affine Systems With Both Input and Output Quantization

Abstract

This technical note is concerned with the problem of simultaneous design of observers and controllers for a class of piecewise-affine systems against signal quantization occurring in both measurement output and control input channels. The general scenario is considered that system state and estimated state may not be in the same operating region. By a novel quantization-error-dependent Lyapunov function, the stability and $\mathcal {H}_{\infty }$ performance criteria are first established for the augmented system composed of a closed-loop control system and an estimation error system with the aid of $S$ -procedure involving the region partition information of the original system. Then, by the cone complementary linearization algorithm, the desired observer and controller gains are solved simultaneously such that the resulting closed-loop system is asymptotically stable with a prescribed $\mathcal {H}_{\infty }$ performance index. Finally, a networked single-link robot arm is utilized to demonstrate the effectiveness of the proposed control strategy.