Small gain theorems for general networks of heterogeneous\n infinite-dimensional systems

2019/01/11 by Andrii Mironchenko, Mironchenko, Andrii · 2 citations
Engineering · #Stability and Control of Uncertain Systems #Control and Stability of Dynamical Systems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1901.03747

Abstract

We prove a small-gain theorem for interconnections of n nonlinear\nheterogeneous input-to-state stable (ISS) control systems of a general nature,\ncovering partial, delay and ordinary differential equations. Furthermore, for\nthe same class of control systems, we derive small-gain theorems for asymptotic\ngain, uniform global stability and weak input-to-state stability properties. We\nshow that our technique is applicable for different formulations of ISS\nproperty (summation, maximum, semimaximum) and discuss tightness of achieved\nsmall-gain theorems. Finally, we introduce variations of uniform asymptotic\ngain and uniform limit properties, which are particularly useful for small-gain\narguments and characterize ISS in terms of these notions.\n

Cited by

• A Lyapunov-Based Small-Gain Theorem for Fixed-Time ISS: Theory, Optimization, and Games
• A Lyapunov-Based Small-Gain Theorem for Fixed-Time Stability

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