• Journal of the Chungcheong Mathematical Society
• /
• v.22 no.1
• /
• pp.49-63
• /
• 2009

We obtain some retarded integral inequalities of Bihari-type and apply these results to a retarded differential equation of Bernoulli-type.

• Journal of the Chungcheong Mathematical Society
• /
• v.27 no.3
• /
• pp.495-502
• /
• 2014

In this paper, we show the ${\psi}$-uniform stability for linear impulsive differential equations and their perturbations by using the impulsive Gronwall's inequalities.

• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.4
• /
• pp.935-943
• /
• 2011

We study the h-stability for linear impulsive differential equations and their perturbations by using the impulsive integral inequalities.

• Journal of the Chungcheong Mathematical Society
• /
• v.28 no.4
• /
• pp.583-590
• /
• 2015

This paper deals with linear impulsive fractional differential equations involving the Caputo derivative with non-integer order q. We provide exact solutions of linear impulsive fractional differential equations with constant coefficient by mean of the Mittag-Leffler functions. Then we apply the exact solutions to improve impulsive integral inequalities with singularity.

• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.2
• /
• pp.393-400
• /
• 2011

In this paper we study h-stability for the linear impulsive equations using the notion of kinematical similarity and impulsive integral inequality.

• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.4
• /
• pp.811-819
• /
• 2013

In this paper we investigate h-stability for linear impulsive equations using the notion of $t_{\infty}$-similarity and an impulsive integral inequality.

• Journal of the Korean Mathematical Society
• /
• v.56 no.1
• /
• pp.127-147
• /
• 2019

In this paper we establish some new explicit solutions for impulsive linear fractional differential equations with impulses at fixed times, which provides a handy tool in deriving singular integral-sum inequalities and an impulsive fractional comparison principle. Thus we study the Mittag-Leffler stability of impulsive differential equations with the Caputo fractional derivative by using the impulsive fractional comparison principle and piecewise continuous functions of Lyapunov's method. Also, we give some examples to illustrate our results.

• The Pure and Applied Mathematics
• /
• v.18 no.4
• /
• pp.329-336
• /
• 2011

Some new Lyapunov-type inequalities for a class of nonlinear differential systems, which are natural refinements and generalizations of the well-known Lyapunov inequality for linear second order differential equations, are given. The results of this paper cover some previous results on this topic.

• KIEE International Transaction on Systems and Control
• /
• v.12D no.1
• /
• pp.39-42
• /
• 2002

This paper focuses on the asymptotic stability of a class of neutral linear systems with mixed time-varying delay arguments. Using the Lyapunov method, a delay-dependent stability criterion to guarantee the asymptotic stability for the systems is derived in terms of linear matrix inequalities (LMIs). The LMIs can be easily solved by various convex optimization algorithms. Two numerical examples are given to illustrate the proposed methods.

• Proceedings of the KSME Conference
• /
• 2004.04a
• /
• pp.828-833
• /
• 2004

The performance of a mixed $H_{\infty}/H_2$ design with pole placement constraints based on robust vibration control for a piezo/beam system is investigated. The governing equation of motion for the piezo/beam system is derived by Hamilton's principle. The assumed mode method is used to discretize the governing equation into a set of ordinary differential equation. A robust controller is designed by $H_{\infty}/H_2$ feedback control law that satisfies additional constraints on the closed-loop pole location in the face of model uncertainties, which are derived for a general class of convex regions of the complex plane. These constraints are expressed in terms of linear matrix inequalities (LMIs) approach for the multiobjective synthesis. The validity and applicability of this approach for vibration suppressions of SMART structural systems are discussed by damping out the multiple vibrational modes of the piezo/beam system.