112 research outputs found
A Corollary for Nonsmooth Systems
In this note, two generalized corollaries to the LaSalle-Yoshizawa Theorem
are presented for nonautonomous systems described by nonlinear differential
equations with discontinuous right-hand sides. Lyapunov-based analysis methods
are developed using differential inclusions to achieve asymptotic convergence
when the candidate Lyapunov derivative is upper bounded by a negative
semi-definite function
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
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