A Lyapunov-Based Small-Gain Theorem for a Network of Finite-Time Input-to-State Stable Systems
Huanhuan Li, Tengfei Liu, Zhong‐Ping Jiang
Abstract
This article presents a Lyapunov formulation of the small-gain theorem for the finite-time input-to-state stability (FTISS) of an interconnected nonlinear system composed of two or more FTISS subsystems. In addition, an FTISS-Lyapunov function for the interconnected system is constructed from the FTISS-Lyapunov functions of the subsystems. With respect to the previously developed nonlinear, Lyapunov-based small-gain theorem restricted to input-to-state stability, a new power-function-based scaling technique is proposed to deal with the challenge that a nonlinearly scaled FTISS-Lyapunov function may not retain a decreasing rate as a power function with a positive power less than one.
Topics & Concepts
Lyapunov functionLyapunov redesignLyapunov exponentControl theory (sociology)Small-gain theoremLyapunov equationControl-Lyapunov functionLyapunov optimizationMathematicsNonlinear systemLyapunov stabilityStability (learning theory)Applied mathematicsComputer scienceControl (management)PhysicsQuantum mechanicsMachine learningArtificial intelligenceStability and Control of Uncertain SystemsControl and Stability of Dynamical SystemsNeural Networks Stability and Synchronization