Decentralized Parametric Stabilization of Quantized Interconnected Systems with Application to Coupled Inverted Pendulums

This paper studies the analysis of parametric stability and decentralized state feedback control of a kind of quantized interconnected systems. The output of each controller is quantized logarithmically before it is input to the subsystem, and the quantized density would affect the stability of the systems. First, a decentralized state feedback controller is designed for interconnected systems without quantization and the corresponding stable region is obtained. Second, for a given controller, the lower bound of the quantization density is evaluated from parameters of local controllers. Finally, the proposed method is applied to coupled inverted pendulums systems which can be viewed as quantized interconnected systems. The simulation results show that by using the proposed quantized controllers, the interconnected inverted pendulum systems are parametrically stabilized.