Scaled Small-Gain Approach to Robust Control of LPV Systems with Uncertain Varying Delay

Time-delay linear parameter-varying (LPV) systems with varying uncertainty in the delay are subject to performance degradation and instability. In this line, we investigate the stability of such systems invoking an input-output stability approach. By considering explicit bounds on the delay rate and time-varying delay uncertainty, the scaled small-gain theorem is adopted to form an interconnected time-delay LPV system for the uncertain dynamics. For such an interconnected time-delay LPV system subject to external disturbances, a Lyapunov-Krasovskii functional (LKF) is proposed whose derivative is augmented with terms resulted from the descriptor method. Then, stability analysis, along with control synthesis conditions, characterized via a prescribed induced L-2-norm of the closed-loop system, are derived in a convex linear matrix inequality (LMI) setting. As a benchmark problem, we examine the automated mean arterial blood pressure (MAP) control in a hypotensive patient where the MAP response dynamics to drug infusion is characterized in a time-delay LPV representation. Finally, closed-loop simulation results are provided to assess the proposed methodology's performance.