Stability Analysis of Discrete-time Lure Systems with Slope-restricted Odd Monotonic Nonlinearities

Abstract— Many nonlinear dynamical systems can be written as Lur’e systems, which are described by a linear time-invariant system interconnected with a diagonal static sector-bounded nonlinearity. Sufficient conditions are derived for the global asymptotic stability analysis of discrete-time Lur’e systems in which the nonlinearities have restricted slope and/or are odd, which is the usual case in real applications. A Lur’ePostnikov-type Lyapunov function is proposed that is used to derive sufficient analysis conditions in terms of linear matrix inequalities (LMIs). The derived stability critera are provably less conservative than criteria published in the literature, with numerical examples indicating that conservatism can be reduced by orders of magnitude.