Extension of the concept of random polytopes and robust stabilization synthesis

In this paper, we introduce families of what we call random polytopes, which are defined through random matrices. Then, we discuss robustly stabilizing state feedback synthesis for discrete-time plants whose dynamics are characterized by the families. Random polytopes enable us to deal with uncertainties in the distributions underlying stochastic systems. Through extending the concept of the polytopes (from the viewpoint of probability measures), we develop a framework of robust stabilization synthesis that can tackle larger classes of uncertainties in the distributions.