A separation theorem for robust pole placement of discrete-time linear control systems with full-order observers

In this paper, we derive a separation theorem for robust pole placement of discrete-time linear control systems with full-order observers. This separation theorem basically demonstrates that we can realize robust pole placement in an nn-dimensional multivariable discrete-time linear control system using a full-order observer-based state feedback control law by means of solving two separate nn-dimensional robust pole placement problems. This paper is a discrete-time version of the work by Duan et al. [G. Duan, S. Thompson, G. Liu, Separation principle for robust pole assignment — An advantage of full-order state observers, in: Proc. 38th IEEE Conf. Decision & Control, Phoenix, Arizona, 1999, pp. 76–78].