Compositional stability of approximately symmetric systems: Initial results

This paper considers nonlinear control systems that are approximately symmetric, and extends some prior work of the author related to stability of symmetric systems to the case where the system is not exactly symmetric. Many engineering systems are composed of components that are nominally identical, but due inherent variability in physical systems, can not be exactly symmetric. By exploiting the baseline symmetric structure of the system and constraining the deviations from exact symmetry, stability results are derived that are independent of the number of components in the system. This paper specifically focuses on the application of LaSalle´s Invariance Principle to approximately symmetric systems, which has broad applicability. The main utility of the stability result is one of scalability or compositionality because the main result shows that if the system is stable for a given number of components, under appropriate conditions, stability is then guaranteed for a larger system composed of the same type of components which are interconnected in a manner consistent with the smaller system.