Title: On the stability of switched semi-active controllers in automotive suspensions

Authors: Sagiv Bar David; Ben Zion Bobrovsky

Addresses: School of Electrical Engineering – Systems, Tel Aviv University, Tel Aviv 6997801, Israel ' School of Electrical Engineering – Systems, Tel Aviv University, Tel Aviv 6997801, Israel

Abstract: The goal of this paper is to present a formal stability analysis of several switched semi-active suspension controllers, either piecewise-linear or completely nonlinear, including the well-known classic Skyhook damping scheme. Although practitioners of semi-active control are familiar with design limitations, owing to the switching effect, these limitations are non-intuitive in general. According to switched systems theory, the stability of a switched control system is by definition not guaranteed, even in a case where all sub-states are independently asymptotically stable. Unconditional Lyapunov stability proofs for the most common piecewise-linear and nonlinear switched controllers are derived analytically, and supporting numerical Lyapunov function simulations are performed. Overall, the global uniform asymptotic stability (GUAS) of a variety of common semi-active switched controllers is proven, thereby validating their widespread practical implementation.

Keywords: semi-active suspension; Lyapunov stability; switched control; GUAS; global uniform asymptotic stability; suspension control; vehicle suspension; skyhook damping; nonlinear switched controllers; piecewise-linear switched controllers; simulation.

DOI: 10.1504/IJVD.2016.074417

International Journal of Vehicle Design, 2016 Vol.70 No.2, pp.137 - 156

Available online: 29 Jan 2016 *

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