Input-to-state dynamical stability and its Lyapunov function characterization
Tóm tắt
We present a new variant of the input-to-state stability (ISS) property which is based on using a one-dimensional dynamical system for building the class /spl Kscr//spl Lscr/ function for the decay estimate and for describing the influence of the perturbation. We show the relation to the original ISS formulation and describe characterizations by means of suitable Lyapunov functions. As applications, we derive quantitative results on stability margins for nonlinear systems and a quantitative version of a small gain theorem for nonlinear systems.
Từ khóa
#Stability #Lyapunov method #Polynomials #Automatic control #Communication system control #Observability #Discrete event systems #Sensor systems #ActuatorsTài liệu tham khảo
10.1007/BF01211516
10.1016/S0167-6911(00)00060-8
sepulchre, 1997, Constructive Nonlinear Control, 10.1007/978-1-4471-0967-9
10.1109/9.28018
10.1016/0167-6911(94)00050-6
10.1016/S0167-6911(98)00003-6
sontag, 2000, the iss philosophy as a unifying framework for stability-like behavior, Nonlinear Control in the Year 2000, 2, 443
10.1016/0167-6911(94)00050-6
10.1051/cocv:1997103
grüne, 2002, Asymptotic Behavior of Dynamical and Control Systems Under Perturbation and Discretization, 1783, 10.1007/b83677
10.1016/S0167-6911(99)00044-4
10.1016/0167-6911(96)00021-7
10.1016/S0167-6911(99)00053-5
krstić, 1998, Stabilization of Nonlinear Uncertain Systems
10.1007/BF01211469
federer, 1969, Geometric Measure Theory
10.1137/S0363012993259981
10.1109/9.544001