QCs characterization of robust stability with simultaneous uncertainties in plant and controller

Abstract

Within the frame work of nest algebra, the robust stability of feedback interconnections of time-varying discrete-time systems with combined uncertainties in the plant and controller is derived via quadratic constraint (QC) approach, where the plant and controller are taken from two path connected uncertainty sets with respect to the topology induced by the gap metric. Some sufficient conditions for the existence of complementary QCs for the components of stable uncertain feedback systems are derived. The path-connectedness is established for some uncertainty sets with particular properties. The fundamental robust stability result represents a generalization of the input–output operator robust stability theorem of uncertainties appearing in the plant alone, to include the case of simultaneous uncertainties appearing in the controller.