Design of shifting state-feedback controllers for LPV systems subject to time-varying saturations via parameter-dependent Lyapunov functions

ISA Trans. 2022 Jul;126:213-225. doi: 10.1016/j.isatra.2021.07.025. Epub 2021 Jul 19.

Abstract

This paper considers the problem of designing a shifting state-feedback controller via quadratic parameter-dependent Lyapunov functions (QPDLFs) for systems subject to symmetric time-varying saturations. By means of the linear parameter varying (LPV) framework and the use of the shifting paradigm and the ellipsoidal invariant theory, it is shown that the solution to this problem can be expressed with linear matrix inequalities (LMIs) which can efficiently be solved via available solvers. Specifically, three hyper-ellipsoidal regions are defined in the state-space domain for ensuring that the control action remains in the linearity region of the actuators where saturation does not occur. Furthermore, the closed-loop convergence speed is regulated online according to the instantaneous saturation limit values through the shifting paradigm concept. The main characteristics of the proposed approach are validated by means of two illustrative examples.

Keywords: Actuator saturation; Invariant ellipsoids; Linear matrix inequalities (LMIs); Linear parameter varying (LPV) systems; Shifting paradigm.