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Volume 3,     Number 4,     Fall 1995

 

STABILITY ANALYSIS AND APPLICATIONS
TO LARGE SCALE IMPULSIVE SYSTEMS:
A NEW APPROACH
XINZHI LIU AND ALLAN WILLMS

Abstract. Stability criteria employing a combined estimate of continuous and discrete portions of an impulsive system are established. To show stability for an impulsive system, it is not necessary to find a Lyapunov function whose derivative along the trajectories is negative definite; however, the function must not be allowed to grow too quickly. Herein we have defined and characterized the necessary growth condition on the Lyapunov function. These stability results are then extended to large scale impulsive systems. This extension, although analogous to extensions for purely discrete or purely continuous systems, is not straightforward due to the hybrid nature of the impulsive system and provides some additional difficulties not associated with continuous or discrete systems. Examples are also worked through which show that an impulsive system may exhibit asymptotic stability behavior even when both the corresponding continuous system and the discrete system are unstable.

 

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