An ISS small gain theorem for general networks

S Dashkovskiy, BS Rüffer, FR Wirth - Mathematics of Control, Signals, and …, 2007 - Springer
… version of the nonlinear small gain theorem for the case of more … extension of the known
small gain theorem to larger interconnections is needed. In this paper we obtain this extension

A small-gain theorem for switched interconnected nonlinear systems and its applications

L Long, J Zhao - IEEE Transactions on Automatic Control, 2013 - ieeexplore.ieee.org
… In particular, it is worth pointing out that this paper extends the classical small-gain theorem
for non-switched systems to switched systems based on the popular average dwell time …

Small-gain theory for stability and control of dynamical networks: A survey

ZP Jiang, T Liu - Annual Reviews in Control, 2018 - Elsevier
… This paper provides a personal account of the small-gain theory as a tool for … theory is the
development of a transformative stability criterion known as the classical small-gain theorem

Small-gain theorem for ISS systems and applications

ZP Jiang, AR Teel, L Praly - Mathematics of Control, Signals and Systems, 1994 - Springer
… establish a generalized small-gain theorem (see Theorem 2.1 and Corollary 2.1) and a gain
theorem (see Theorem 2.2). The first one extends the small monotone gain theorem proved …

Adaptive backstepping controller design using stochastic small-gain theorem

ZJ Wu, XJ Xie, SY Zhang - Automatica, 2007 - Elsevier
… In this section, we try to extend the concept of ISpS and the corresponding Lyapunov stability
criterion in Jiang et al. (1994) to stochastic nonlinear systems. For interconnected systems …

Multiple Lyapunov functions-based small-gain theorems for switched interconnected nonlinear systems

L Long - IEEE Transactions on Automatic Control, 2017 - ieeexplore.ieee.org
… For example, the well known ISS small-gain theorem was extended to the case of
switched systems with arbitrary switchings [6]. In [21], a small-gain theorem for switched …

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

A Mironchenko - SIAM Journal on Control and Optimization, 2021 - SIAM
… We prove a small-gain theorem for interconnections of n … systems, we derive small-gain
theorems for asymptotic gain, … , 30] also an extension of the wISS small-gain theorem to the …

[PDF][PDF] The necessity of the small-gain theorem for time-varying and nonlinear systems

JS Shamma - IEEE transactions on automatic control, 1991 - researchgate.net
… In a similar context, the necessity of the smallgain theorem … (LTV) perturbations, and extended
to LTV systems subject to … the small-gain theorem is also necessary, thereby extending

A simplified small gain theorem for time-varying nonlinear systems

Z Chen, J Huang - IEEE Transactions on Automatic Control, 2005 - ieeexplore.ieee.org
… To extend the small gain theorem to uncertain systems, we need to extend the ISS concept
to uncertain system (11). Definition 2.1: System (11) is said to be robustly [with respect to d(t)] …

On a small gain theorem for networks of iISS systems

H Ito, S Dashkovskiy, F Wirth - … of the 48h IEEE Conference on …, 2009 - ieeexplore.ieee.org
… the philosophy of the ISS small-gain theorem has been extended to the iISS … small-gain
theorem has been extended to the case of general networks[7], [17]. The ISS small-gain theorem