  Linear parameter-varying (LPV) systems with uncertainty in time-varying
delays 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 with input and output vectors of the
auxiliary system introduced for the uncertain dynamics. For such an
interconnected time-delay LPV system subject to external disturbances, a
Lyapunov-Krasovskii functional (LKF) is constructed whose derivative is
augmented with the terms resulted from the descriptor method. Then, stability
conditions and a prescribed induced L2-norm in terms of the disturbance
rejection performance are derived in a convex linear matrix inequalities (LMIs)
setting. Subsequently, a congruent transformation enables us to compute a
gain-scheduled state-feedback controller for a class of LPV systems with an
uncertain time-varying delay. As a benchmark, we examine the automated mean
arterial blood pressure (MAP) control in an individual with hypotension where
the MAP response dynamics to drug infusion is characterized in a time-delay LPV
representation. Finally, the closed-loop simulation results are provided to
demonstrate the provided methodology's performance.
