Abstract
In this paper, the input-to-state stability for coupled control systems is investigated. A systematic method of constructing a global Lyapunov function for the coupled control systems is provided by combining graph theory and the Lyapunov method. Consequently, some novel global input-to-state stability principles are given. As an application to this result, a coupled Lurie system is also discussed. By constructing an appropriate Lyapunov function, a sufficient condition ensuring input-to-state stability of this coupled Lurie system is established. Two examples are provided to demonstrate the effectiveness of the theoretical results.
Highlights
In recent years, coupled control systems (CCSs) have received considerable attention for their interesting characteristics from the mathematical point of view
Grüne [ ] presented a new variant of the input-to-state stability (ISS) property which is based on a one-dimensional dynamical system, showed the relation to the original ISS formulation, and described the characterizations by means of suitable Lyapunov functions
Motivated by the above discussions, in this paper, we investigate the ISS of CCSs
Summary
In recent years, coupled control systems (CCSs) have received considerable attention for their interesting characteristics from the mathematical point of view. By constructing an appropriate Lyapunov function, a sufficient condition ensuring the ISS of this coupled Lurie system is established. Fij(xi, xj) are arbitrary functions for any ≤ i, j ≤ l, aij are elements of matrix A, Q is the set of all spanning unicyclic graphs of (G, A), W (Q) is the weight of Q, and CQ denotes the directed cycle of Q.
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