Qualitative analysis of dynamical systems determined by differential inequalities with applications to robust stability

Cooperative Control of Dynamical Systems

“…2 In Section 2.3.2, Theorem 2.8 is used to facilitate stability analysis of nonlinear systems in terms of a Lyapunov function and to determine an explicit upper bound on state trajectory. In such applications as stability of largescale interconnected systems, dynamic coupling among different sub-systems may have certain properties that render the vector inequalities of (2.6) and (2.7) in terms of a vector of Lyapunov functions v k and, if so, Theorem 2.10 can be applied [118,119,156,268]. Later in Section 6.2.1, another comparison theorem is developed for cooperative systems, and it is different from Theorem 2.10 because it does not require the mixed quasi-monotone property.…”