• Kyungpook Mathematical Journal
• /
• v.62 no.3
• /
• pp.455-465
• /
• 2022

We point out a flaw in a result proved by Singh and Shah [Kyungpook Math. J., 57(2017), 537-543] which was recently published in Kyungpook Mathematical Journal. Further, we point out an error in another result of the same paper which we correct and obtain integral extension of the corrected form.

• Journal of Electrical Engineering and Technology
• /
• v.13 no.6
• /
• pp.2521-2529
• /
• 2018

This paper deals with a sampled-data tracking control problem for the Takagi-Sugeno fuzzy system with external disturbances. We derive a stability condition guaranteeing both asymptotic stability and H-infinity tracking performance by employing a newly proposed time-dependent line-integral fuzzy Lyapunov-Krasovskii functional. A new integral inequality is also introduced, by which the proposed stability condition is formulated in terms of linear matrix inequalities. Finally, the effectiveness of the proposed method is demonstrated through a simulation example.

• Communications of the Korean Mathematical Society
• /
• v.38 no.4
• /
• pp.1111-1126
• /
• 2023

In this paper, we define a new subclass of k-uniformly starlike functions of order γ (0 ≤ γ < 1) by using certain generalized q-integral operator. We explore geometric interpretation of the functions in this class by connecting it with conic domains. We also investigate q-sufficient coefficient condition, q-Fekete-Szegö inequalities, q-Bieberbach-De Branges type coefficient estimates and radius problem for functions in this class. We conclude this paper by introducing an analogous subclass of k-uniformly convex functions of order γ by using the generalized q-integral operator. We omit the results for this new class because they can be directly translated from the corresponding results of our main class.

• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.4
• /
• pp.831-842
• /
• 2013

In this paper, we investigate uniform Lipschitz and asymptotic stability for perturbed differential systems using integral inequalities.

• Journal of the Korean Mathematical Society
• /
• v.37 no.4
• /
• pp.613-624
• /
• 2000

We characterize a condition for M to be of weak type ($\Phi$1, $\Phi$2) in terms of Orlicz norms.

• Kyungpook Mathematical Journal
• /
• v.47 no.3
• /
• pp.411-423
• /
• 2007

This paper deals with a reverse Hardy-Hilbert's inequality with a best constant factor by introducing two parameters ${\lambda}$ and ${\alpha}$. We also consider the equivalent form and the analogue integral inequalities. Some particular results are given.

• Bulletin of the Korean Mathematical Society
• /
• v.43 no.1
• /
• pp.27-41
• /
• 2006

A counterpart of the famous Bessel's inequality for orthornormal families in real or complex inner product spaces is given. Applications for some Gruss type inequalities are also provided.

• 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.

• International Journal of Control, Automation, and Systems
• /
• v.5 no.2
• /
• pp.117-127
• /
• 2007

Many real world control systems usually track several control objectives, simultaneously. At the moment, it is desirable to meet all specified goals using the controllers with simple structures like as proportional-integral (PI) and proportional-integral-derivative (PID) which are very useful in industry applications. Since in practice, these controllers are commonly tuned based on classical or trial-and-error approaches, they are incapable of obtaining good dynamical performance to capture all design objectives and specifications. This paper addresses a new method to bridge the gap between the power of optimal multiobjective control and PI/PID industrial controls. First the PI/PID control problem is reduced to a static output feedback control synthesis through the mixed $H_2/H_{\infty}$ control technique, and then the control parameters are easily carried out using an iterative linear matrix inequalities (ILMI) algorithm. Numerical examples on load-frequency control (LFC) and power system stabilizer (PSS) designs are given to illustrate the proposed methodology. The results are compared with genetic algorithm (GA) based multiobjective control and LMI based full order mixed $H_2/H_{\infty}$ control designs.

• Journal of the Korean Mathematical Society
• /
• v.43 no.5
• /
• pp.911-929
• /
• 2006

A refinement of $Gr\ddot{u}ss$ type inequality for the Bochner integral of vector-valued functions in real or complex Hilbert spaces is given. Related results are obtained. Application for finite Fourier transforms of vector-valued functions and some particular inequalities are provided.