Stabilization of Linear Uncertain Discrete-Time Systems with Nonlinear Actuators

A robust stabilization condition which guarantees the robust stability of multivariable uncertain discrete-time systems under state feedback with a class of nonlinear actuators is derived in the time domain. A simple method recently developed for synthesizing controllers for robust pole assignment of linear uncertain systems is extended to obtain the robust stabilization condition. In this paper, the plant is not restricted to the stable case. Moreover, based on the robust stabilization condition, an algorithm is proposed for determining the tolerable operational sectors of nonlinear actuators for the case where the robust controller is designed first in order that the feedback system without nonlinear actuators is asymptotically stable. As long as the nonlinear actuators lie in the determined tolerable operational sectors, the linear multivariable uncertain discrete-time systems with these nonlinear actuators and the designed robust controller are still asymptotically stable. An example is given to demonstrate the use of the proposed approach.