• KIEE International Transaction on Systems and Control
• /
• v.2D no.2
• /
• pp.92-96
• /
• 2002

This paper is concerned with properties of a Lyapunov functional of state delay systems. It is shown that if a state delay system has a pure imaginary pole for some state delay, then no Lyapunov functional satisfying a Lyapunov condition exists periodically with respect to change of the state delay. This periodic property is unique in state delay systems and has been well known in the frequency domain stability conditions. However, in the time domain stability conditions using a Lyapunov functional, the periodic property is not known explicitly.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.60 no.3
• /
• pp.620-624
• /
• 2011

This paper propose a new delay-dependent stability criterion of neutral time-delay systems. By employing double-integral terms in augmented states and constructing a new Lyapunov-Krasovskii's functional, a delay-dependent stability criterion is established in terms of Linear Matrix Inequality. Through numerical examples, the validity and improvement results obtained by applying the proposed stability criterion will be shown.

• Korean Journal of Mathematics
• /
• v.21 no.3
• /
• pp.345-350
• /
• 2013

Some results on the sensitivity of the solution of the generalized Lyapunov equation $$A^{n-1}X+A^{n-2}XA^*+{\cdots}+X(A^*)^{n-1}=B$$ are shown follow easily from well-known theorems in functional analysis.

• Journal of applied mathematics & informatics
• /
• v.30 no.5_6
• /
• pp.741-748
• /
• 2012

In this work, we prove the instability of solutions for a class of nonlinear functional differential equations of the eighth order with n-deviating arguments. We employ the functional Lyapunov approach and the Krasovskii criteria to prove the main results. The obtained results extend some existing results in the literature.

• 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.

• Journal of applied mathematics & informatics
• /
• v.28 no.1_2
• /
• pp.295-309
• /
• 2010

In this paper, we study delayed high-order Cohen-Grossberg neural networks with reaction-diffusion terms and Neumann boundary conditions. By using inequality techniques and constructing Lyapunov functional method, some sufficient conditions are given to ensure the existence and convergence of the periodic oscillatory solution. Finally, an example is given to verify the theoretical analysis.

• Journal of the Korean Mathematical Society
• /
• v.48 no.2
• /
• pp.223-240
• /
• 2011

In this paper, the problem on periodic solutions of the bidirectional associative memory neural networks with both periodic coefficients and periodic time-varying delays is discussed. By using degree theory, inequality technique and Lyapunov functional, we establish the existence, uniqueness, and global asymptotic stability of a periodic solution. The obtained results of stability are less restrictive than previously known criteria, and the hypotheses for the boundedness and monotonicity on the activation functions are removed.

• Journal of applied mathematics & informatics
• /
• v.29 no.1_2
• /
• pp.103-117
• /
• 2011

By using an important lemma, some analysis techniques and Lyapunov functional method, we establish the sufficient conditions of the existence of equilibrium solution of a class of BAM neural network with impulses and distributed delays. Finally, applications and an example are given to illustrate the effectiveness of the main results.

• Journal of applied mathematics & informatics
• /
• v.18 no.1_2
• /
• pp.261-272
• /
• 2005

In this paper, boundedness criteria are established for solutions of a class of impulsive functional differential equations with infinite delays of the form $x'(t) = F(t, x(\cdot)), t > t^{\ast} {\Delta}x(t_{k})= I(t_{k}, x(t_{k}^{-})), k = 1,2,...$ By using Lyapunov functions and Razumikhin technique, some new Razumikhin-type theorems on boundedness are obtained.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.56 no.9
• /
• pp.1648-1654
• /
• 2007

In this paper, we consider the design of $H_\infty$ high-gain state feedback control for time-delayed linear systems with limited actuator capacities. The high-gain control means that the control permits the predetermined degree of saturation. Based on new Lyapunov-Krasovskii functional, we derive a result in the form of matrix inequalities. The matrix inequalities are consisted of LMIs those confirm the positive definiteness of Lyapunov- Krasovskii functional, satisfaction of predetermined degree of saturation, reachable set and $L_2$ gain constraint. The result is dependent on the bound of time-delay and its rate, predetermined degree of saturation, actuator capacity, and the allowed size of disturbances. Finally, we give a numerical example to show the effectiveness and usefulness of our result.