A Generalized Sector Condition Approach to Observer-Based Control of Input-Delay LPV Systems under Saturation and Matched Disturbances

Abstract

The control design for parameter-dependent input-delay linear parameter-varying (LPV) systems with saturation constraints and matched input disturbances is examined in this paper. A gain-scheduled dynamic output feedback controller coupled with a disturbance observer to cancel out input disturbance effects, is augmented with an anti-windup compensator to locally stabilize the input-delay LPV system under saturation, model uncertainty, and exogenous disturbances. Sufficient delay-dependent conditions to asymptotically stabilize the closed-loop system are derived using Lyapunov-Krasovskii functionals and a modified generalized sector condition to address the input saturation nonlinearity. The level of disturbance rejection is characterized via the closed-loop induced <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm of the closed-loop system in the form of linear matrix inequality (LMI) constraints. The results are examined in the context of the mean arterial pressure (MAP) control in the clinical resuscitation of hypotensive patients. The MAP variation response to the injection of vasopressor drugs is modeled as an LPV system with a varying input delay, and is susceptible to model uncertainty and input/output disturbances. A Bayesian filtering method known as the cubature Kalman filter (CKF) is used to estimate the instantaneous values of the parameters. The varying delay is estimated via a multiple-model approach. The proposed input-delay LPV control is validated in closed-loop simulations to demonstrate its merits and capabilities in the presence of drug administration constraints.