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

• Published in: Proceedings of the American Control Conference pp. 4912 - 4919
• Main Authors: Tasoujian, Shahin, Salavati, Saeed, Grigoriadis, Karolos, Franchek, Matthew
• Format: Conference Proceeding
• Language: English
• Published: American Automatic Control Council 25.05.2021
• Subjects: Arterial blood pressure; Delays; Drugs; Simulation; Stability analysis; Sufficient conditions; Uncertainty
• ISSN: 2378-5861
• DOI: 10.23919/ACC50511.2021.9482658

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 \mathcal{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.