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

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.