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arXiv · 2502.06770

Parameter-Dependent Control Lyapunov Functions for Stabilizing Nonlinear Parameter-Varying Systems

Pan Zhao
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Abstract

This paper introduces the concept of parameter-dependent (PD) control Lyapunov functions (CLFs) for gain-scheduled stabilization of nonlinear parameter-varying (NPV) systems. It shows that given a PD-CLF, a min-norm control law can be constructed by solving a robust quadratic program. For polynomial control-affine NPV systems, it provides convex conditions, based on the sum of squares programming, to jointly synthesize a PD-CLF and a PD controller while maximizing the PD region of stabilization. Input constraints can be straightforwardly incorporated into the synthesis procedure. Unlike traditional linear parameter-varying (LPV) methods that rely on linearization or over-approximation to get an LPV model, the proposed framework fully captures the nonlinearities of the system dynamics. The theoretical results are validated through numerical simulations, including a 2D rocket landing case study under varying mass and inertia.

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Pan Zhao. 2025-02-10. Parameter-Dependent Control Lyapunov Functions for Stabilizing Nonlinear Parameter-Varying Systems. https://arxiv.org/abs/2502.06770

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