Robust Stabilization of LPV Sampled-Data Systems via Quadratic Polynomial Conditions

This work addresses the robust stabilization of linear parameter-varying (LPV) systems with state feedback, using linear matrix inequalities (LMIs) for the synthesis of sampled-data controllers. Using the input-delay approach, we propose a looped-functional whose time derivative is a quadratic polynomial. The negativity of this polynomial must be ensured to certify the closed-loop stability. Pólya's Theorem is then employed to ensure the negativity of quadratic functions, yielding new and less conservative convex conditions for controller synthesis under time-varying sampling intervals. Numerical examples illustrate the effectiveness of the proposed technique, showing that the new design conditions outperform those reported in recent literature. Finally, the proposed design conditions are adapted to handle quasi-LPV systems and applied to a nonlinear level control system. Experimental tests on the system illustrate the performance of the designed controller for different time-varying sampling intervals.