Abstract
The present work examines the delay-dependent gain-scheduling feedback control with guaranteed closed-loop stability and induced L2 norm performance for continuous-time linear parameter-varying (LPV) systems with arbitrary time-varying delay. An extension of Lyapunov stability utilizing Krasovskii functionals is considered to derive stability analysis and synthesis conditions for delay-dependent dynamic output feedback LPV control design. The main challenges associated with this approach are selecting appropriate Lyapunov-Krasovskii functionals (LKFs) and finding efficient integral inequalities to bound the derivative of the LKF. Accordingly, a novel modified parameter-dependent LKF candidate along with an affine version of Jensen’s inequality bounding technique are employed leading to the derivation of less conservative sufficient conditions expressed in terms of convex linear matrix inequalities (LMIs). The proposed methodology is compared with past work in the literature in terms of conservatism reduction and performance improvement through a numerical example. Finally, the application of the proposed output-feedback LPV control design is evaluated on the automated mean arterial blood pressure (MAP) regulation in critical patient resuscitation via vasoactive drug infusion. Closed-loop simulation results are presented to illustrate the potential of the introduced LPV gain-scheduling design to provide MAP set-point tracking in the presence of disturbances and varying input delays.
Highlights
Linear parameter-varying (LPV) systems are linear dynamical systems whose dynamic characteristics depend on a time-varying measurable scheduling parameter vector
In the mean arterial blood pressure (MAP) dynamics LPV model Eq 31, the performance controlled output vector is defined as z(t) [φ · xe(t) ψ · u(t)]T where the tracking error, xe(t), and the control effort, u(t), are penalized by the weighting scalars φ and ψ, respectively
An improved parameter-dependent Lyapunov Krasovskii functional (LKF) candidate was proposed, followed by an efficient bounding technique using the affine Jensen’s inequality, for the design of output-feedback LPV controllers. This choices of Lyapunov-Krasovskii functionals (LKFs) and integral inequality constraints reduced the conservatism of the method by limiting the bounding gap in the integral cross-terms of the LKF derivative
Summary
Linear parameter-varying (LPV) systems are linear dynamical systems whose dynamic characteristics depend on a time-varying measurable scheduling parameter vector In this context of the LPV systems framework, the scheduling parameter vector captures the dynamics of nonlinear or time-varying systems in a systematic fashion (Briat, 2014) and has found applications in flight control (Lu et al, 2006), automotive systems (Tasoujian et al, 2016; Salavati et al, 2019), energy (Bianchi et al, 2005), and biomedical systems (Colmegna et al, 2015; Tasoujian et al, 2019b). Traditional gain-scheduling controllers are designed by interpolation of separately designed controllers for the system’s operation points Such design methods suffer from implementation difficulties and lack of closed-loop stability and performance guarantees (Shamma and Athans, 1990; Bianchi et al, 2006). Time-delay is a source of instability and performance degradation
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