Stability Analysis for a Class of Systems: From Model-Based Methods to Data-Driven Methods

This paper presents some new methods to analyze the stability of the equilibrium point, and the bounded-input/bounded-state (BIBS) and the bounded-input/bounded-output (BIBO) stabilities for linear systems and a class of nonlinear systems. We study these systems in both continuous-time and discrete-time forms, using approaches from model-based methods to data-driven methods. For linear systems, our work about the BIBS and the BIBO stabilities does not concern the state controllability or the state observability. The data-driven methods can analyze the stabilities by doing some simple experiments and observations, while not identifying the corresponding parameter matrices. Our methods are easier to understand and more convenient to use in engineering practice.