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An ISS small gain theorem for general networks. (English) Zbl 1125.93062
The paper deals with nonlinear dynamical system which consists of two or more input-to-state stability (ISS) subsystems. The aim is to obtain conditions for reduction the stability problem of the overall system to consideration of subsystems stability. The approach applies asymptotic gains and global stability to prove the ISS results for general interconnected system. The results proved generalize the known small gain theorems. Also the special case of linear gains is considered. In particular, it is shown that the small gain condition is closely connected with stability of a discrete time monotone dynamical system defined by use of gain matrix.
93D25Input-output approaches to stability of control systems
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