Stability Analysis of Discrete-time Lure Systems with Slope-restricted Odd Monotonic Nonlinearities
For control engineers analyzing stability of discrete-time nonlinear systems, this provides a practical improvement over existing LMI-based criteria.
This paper derives less conservative sufficient conditions for global asymptotic stability of discrete-time Lure systems with slope-restricted odd monotonic nonlinearities, using a Lure-Postnikov-type Lyapunov function and LMIs. Numerical examples show conservatism reduction by orders of magnitude.
Many nonlinear dynamical systems can be written as Lure 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 Lure systems in which the nonlinearities have restricted slope and/or are odd, which is the usual case in real applications. A Lure-Postnikov-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.