A Less Conservative Stability Criterion for Discrete-Time Lur'e Systems With Sector and Slope Restrictions

This paper proposes a less conservative stability criterion for discrete-time Lur'e systems with sector and slope restrictions by constructing a novel Lyapunov functional. Compared with the Lyapunov functional in the literature, this paper fully utilizes the sector and slope restrictions to the novel Lyapunov functional which includes integral terms involved with the sector restriction of the nonlinearities $\phi(y_{i})$ and $\phi(y_{i+1})$ , integral terms involved with the slope restriction between $\phi(y_{i})$ and $\phi(y_{i+1})$ , and a quadratic term with an augmented vector related to available vectors for representing upper and lower bounds of all integral terms. The positive definiteness of a matrix appearing in the quadratic term can be relaxed by utilizing the lower bounds of all integral terms. Based on the novel Lyapunov functional, an improved stability criterion is derived in terms of linear matrix inequalities. Numerical examples show the effectiveness of the proposed criterion.