40,394 research outputs found
A Small-Gain Theorem with Applications to Input/Output Systems, Incremental Stability, Detectability, and Interconnections
A general ISS-type small-gain result is presented. It specializes to a
small-gain theorem for ISS operators, and it also recovers the classical
statement for ISS systems in state-space form. In addition, we highlight
applications to incrementally stable systems, detectable systems, and to
interconnections of stable systems.Comment: 16 pages, no figure
Feedback Stabilization Methods for the Numerical Solution of Systems of Ordinary Differential Equations
In this work we study the problem of step size selection for numerical
schemes, which guarantees that the numerical solution presents the same
qualitative behavior as the original system of ordinary differential equations,
by means of tools from nonlinear control theory. Lyapunov-based and Small-Gain
feedback stabilization methods are exploited and numerous illustrating
applications are presented for systems with a globally asymptotically stable
equilibrium point. The obtained results can be used for the control of the
global discretization error as well.Comment: 33 pages, 9 figures. Submitted for possible publication to BIT
Numerical Mathematic
A Unified Approach to High-Gain Adaptive Controllers
It has been known for some time that proportional output feedback will
stabilize MIMO, minimum-phase, linear time-invariant systems if the feedback
gain is sufficiently large. High-gain adaptive controllers achieve stability by
automatically driving up the feedback gain monotonically. More recently, it was
demonstrated that sample-and-hold implementations of the high-gain adaptive
controller also require adaptation of the sampling rate. In this paper, we use
recent advances in the mathematical field of dynamic equations on time scales
to unify and generalize the discrete and continuous versions of the high-gain
adaptive controller. We prove the stability of high-gain adaptive controllers
on a wide class of time scales
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