Abstract
This paper considers the finite-time stability of linear time-varying singular impulsive systems. A lemma which states an important inequality was first established. Then some sufficient conditions for the systems to be finite-time stable were derived. The proposed results remove some restrictions of the existing methods and thus can be applied to more general systems. Finally, a numerical example was presented to illustrate the proposed approaches. Key words: Singular impulsive systems, finite-time stability, comparison principle.
Highlights
Singular systems are referred to as descriptor, semistate, implicit, constrained, differential-algebraic equation, or generalized state-space systems and arise naturally in many practical applications (Campbell, 1980)
This paper considers the finite-time stability of linear time-varying singular impulsive systems
A stable system might be useless because the stable domain or the domain of the desired attractor is not large enough and on the other hand, sometimes an unstable system may be acceptable since the system oscillates sufficiently near the desired state on a predefined finite time interval
Summary
Singular systems are referred to as descriptor, semistate, implicit, constrained, differential-algebraic equation, or generalized state-space systems and arise naturally in many practical applications (Campbell, 1980). This paper considers the finite-time stability of linear time-varying singular impulsive systems. In Zhao et al (2008), finite-time stability of linear timevarying singular impulsive systems is defined and some sufficient conditions are derived. We aimed to study the finite-time stability of linear time-varying singular impulsive systems and try to remove the above mentioned restrictions.
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