State Feedback Control of Discrete-Time Lur'e Systems with Sector-Bounded Slope-Restricted Nonlinearities

The global asymptotic stability analysis and state feedback control design for Lur'e systems are formulated in terms of linear and bilinear matrix inequalities (LMIs and BMIs), respectively, for static nonlinearities that are both sector-bounded and slope-restricted. The LMI problem is solvable in polynomial time using standard solvers, and suboptimal solutions to the BMI problem can be obtained by iteratively solving LMI problems. In three numerical examples from the literature, the LMI stability condition is observed to produce stability margins that are either the same or less conservative than published stability criteria. In another example, the iterative-LMI method is used to design a state feedback controller that is guaranteed to provide global asymptotic stability for the closed-loop system.