State-Compensation-Linearization-Based Stability Margin Analysis for a Class of Nonlinear Systems: A Data-Driven Method

Abstract: The classical stability margin analysis based on the linearized model is widely used in practice even in nonlinear systems. Although linear analysis techniques are relatively standard and have simple implementation structures, they are prone to misbehavior and failure when the system is performing an off-nominal operation. To avoid the drawbacks and exploit the advantages of linear analysis methods and frequency-domain stability margin analysis while tackling system nonlinearity, a state-compensation-linearization-based stability margin analysis method is studied in the paper. Based on the state-compensation-linearization-based stabilizing control, the definition and measurement of the stability margin are given. The l2 gain margin and l2 time-delay margin for the closed-loop nonlinear system with state-compensation-linearization-based stabilizing control are defined and derived approximatively by the small-gain theorem in theory. The stability margin measurement can be carried out by the frequency-sweep method in practice. The proposed method is a data-driven method for obtaining the stability margin of nonlinear systems, which is practical and can be applied to practical systems directly. Finally, three numerical examples are given to illustrate the effectiveness of the proposed method.