Saturating Sampled-Data Control Design for Lur’e Systems
Résumé
This paper addresses the problem of designing saturating sampled-data control laws for Lur'e type systems. The closed-loop system is modeled as an hybrid system to formally take into account the aperiodic sampling phenomenon and a control law that depends on the time elapsed between two consecutive sampling instants. This control law considers a nonlinear feedback of the sampled state and the previous value of the control signal. Under this setup and the use of timerdependent quadratic Lyapunov functions, regional stabilizing conditions are proposed as timer-dependent linear matrix inequalities (LMIs). Considering an affine timer dependency, an optimization problem based on semi-definite programming is proposed to compute the control law gains aiming at enlarging an estimate of the region of attraction of the closed-loop system. A numerical example illustrates the application of the proposed results.
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