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Zbl 1125.93062
Dashkovskiy, Sergey; Rüffer, Björn S.; Wirth, Fabian R.
An ISS small gain theorem for general networks. (English)
[J] Math. Control Signals Syst. 19, No. 2, 93-122 (2007). ISSN 0932-4194; ISSN 1435-568X/e

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.
[Alexander Mikhailovich Kovalev (Donetsk)]

MSC 2000:: *93D25 Input-output approaches to stability of control systems
93C15 Control systems governed by ODE
93C10 Nonlinear control systems
93-01 Textbooks (systems and control)

Keywords: Interconnected systems; Input-to-scate stability; Small gain theorem; Large-scale systems; Monotone maps

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Zentralblatt MATH Berlin [Germany]