Robust Analysis of Discrete–time Lur’e Systems with Slope Restrictions Using Convex Optimization

This paper considers robust stability and robust performance analysis for discrete-time linear systems subject to nonlinear uncertainty. The uncertainty set is described by memoryless, time-invariant, sector bounded, and slope restricted nonlinearities. We first give an overview of the absolute stability criterion based on the Lur’e-Postkinov Lyapunov function, along with a frequency domain condition. Subsequently, we derive sufficient conditions to compute the upper bounds of the worst case H2 and worst case H∞ performance. For both robust stability testing and robust performance computation, we show that these sufficient conditions can be readily and efficiently determined by performing convex optimization over linear matrix inequalities.