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Changing supply functions in input/state stable systems. (English) Zbl 0832.93047
The authors consider the system x ˙=f(x,u), f: n × m n , locally Lipschitz with f(0,0)=0. The system is ISS if there exists a positive definite V(x), V(0)=0, radially bounded n (a storage function) and two functions (in K ) α and γ such that V ˙=(V·f)γ(|u|)-α(|x|). A combination of the γ and α functions characterizes the “input to gain” for the system. The authors prove some relations for positive definiteness of the storage function and the existence of K functions assuring that dissipation estimates for some composite systems are available.
93D10Popov-type stability of feedback systems
93C10Nonlinear control systems
93A99General systems theory