Conclusion
Lyapunov-based stability of dynamical systems

This article presented an analysis of nonlinear dynamic systems. Various concepts of stability were introduced, such as attractivity, stability in the strict sense, and asymptotic stability via estimates along solutions or via comparison functions. Lyapunov’s theory was then reviewed, providing sufficient conditions for stability and for asymptotic stability. For linear systems, it provides numerically verifiable necessary and sufficient conditions, as illustrated by the inverted pendulum. Next, an intermediate case was studied in greater detail—specifically, systems with isolated nonlinearity, such as those resulting from a linear dynamic model with a saturated input. This article concluded with a discussion of developments in Lyapunov theory for studying the performance and robustness of linear and nonlinear systems.

The Lyapunov-based approach has enabled the development of results for...