Piecewise Quantization-Dependent Approach to Quantized Stabilization of Piecewise-Affine Systems

This paper studies the stability and stabilization problems for discrete-time piecewise-affine (PWA) systems with single input-and-state quantization. The PWA controller is considered to be dependent on the controlled PWA system modes; the adopted logarithmic quantizers are in a piecewise form, which is synchronized with the operating mode of the PWA system. A piecewise Lyapunov function is constructed, which has dependence on the sector-bounded uncertainties of both the control input and the state-feedback signal. Afterward, stability and stabilization criteria are derived based on the constructed Lyapunov function. The proposed quantized control strategy is illustrated via an application to a simulated temperature control problem.