1,430 research outputs found
On reduction of differential inclusions and Lyapunov stability
In this paper, locally Lipschitz, regular functions are utilized to identify
and remove infeasible directions from set-valued maps that define differential
inclusions. The resulting reduced set-valued map is point-wise smaller (in the
sense of set containment) than the original set-valued map. The corresponding
reduced differential inclusion, defined by the reduced set-valued map, is
utilized to develop a generalized notion of a derivative for locally Lipschitz
candidate Lyapunov functions in the direction(s) of a set-valued map. The
developed generalized derivative yields less conservative statements of
Lyapunov stability theorems, invariance theorems, invariance-like results, and
Matrosov theorems for differential inclusions. Included illustrative examples
demonstrate the utility of the developed theory
Time-Varying Input and State Delay Compensation for Uncertain Nonlinear Systems
A robust controller is developed for uncertain, second-order nonlinear
systems subject to simultaneous unknown, time-varying state delays and known,
time-varying input delays in addition to additive, sufficiently smooth
disturbances. An integral term composed of previous control values facilitates
a delay-free open-loop error system and the development of the feedback control
structure. A stability analysis based on Lyapunov-Krasovskii (LK) functionals
guarantees uniformly ultimately bounded tracking under the assumption that the
delays are bounded and slowly varying
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