On the Stability of Nonlinear Minimum Variance Control for a Second-Order Volterra Series Model

Abstract

In this paper, the stability of a closed-loop system with nonlinear minimum variance (NMV) controller for a second order Volterra series model is studied. It is shown that the closed-loop system with second-order Volterra series model and minimum variance control signal is a state-dependent switching system with an arbitrary switching signal. The necessary condition for asymptotic stability of this system is the stability of its all subsystems and is investigated using a linearization approach. Also, a sufficient closed-loop stability condition with NMV control is introduced. It is shown that if the sufficient stability condition is violated, it can be satisfied by using a generalized output and nonlinear generalized minimum variance control (NGMV).