1,555 research outputs found
Small gain theorems for large scale systems and construction of ISS Lyapunov functions
We consider interconnections of n nonlinear subsystems in the input-to-state
stability (ISS) framework. For each subsystem an ISS Lyapunov function is given
that treats the other subsystems as independent inputs. A gain matrix is used
to encode the mutual dependencies of the systems in the network. Under a small
gain assumption on the monotone operator induced by the gain matrix, a locally
Lipschitz continuous ISS Lyapunov function is obtained constructively for the
entire network by appropriately scaling the individual Lyapunov functions for
the subsystems. The results are obtained in a general formulation of ISS, the
cases of summation, maximization and separation with respect to external gains
are obtained as corollaries.Comment: provisionally accepted by SIAM Journal on Control and Optimizatio
Global Stabilization of Triangular Systems with Time-Delayed Dynamic Input Perturbations
A control design approach is developed for a general class of uncertain
strict-feedback-like nonlinear systems with dynamic uncertain input
nonlinearities with time delays. The system structure considered in this paper
includes a nominal uncertain strict-feedback-like subsystem, the input signal
to which is generated by an uncertain nonlinear input unmodeled dynamics that
is driven by the entire system state (including unmeasured state variables) and
is also allowed to depend on time delayed versions of the system state variable
and control input signals. The system also includes additive uncertain
nonlinear functions, coupled nonlinear appended dynamics, and uncertain dynamic
input nonlinearities with time-varying uncertain time delays. The proposed
control design approach provides a globally stabilizing delay-independent
robust adaptive output-feedback dynamic controller based on a dual dynamic
high-gain scaling based structure.Comment: 2017 IEEE International Carpathian Control Conference (ICCC
Relaxed ISS Small-Gain Theorems for Discrete-Time Systems
In this paper ISS small-gain theorems for discrete-time systems are stated,
which do not require input-to-state stability (ISS) of each subsystem. This
approach weakens conservatism in ISS small-gain theory, and for the class of
exponentially ISS systems we are able to prove that the proposed relaxed
small-gain theorems are non-conservative in a sense to be made precise. The
proofs of the small-gain theorems rely on the construction of a dissipative
finite-step ISS Lyapunov function which is introduced in this work.
Furthermore, dissipative finite-step ISS Lyapunov functions, as relaxations of
ISS Lyapunov functions, are shown to be sufficient and necessary to conclude
ISS of the overall system.Comment: input-to-state stability, Lyapunov methods, small-gain conditions,
discrete-time non-linear systems, large-scale interconnection
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