• Kyungpook Mathematical Journal
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• v.48 no.1
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• pp.45-61
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• 2008

We investigate the generalized Hyers-Ulam-Rassias stability in p-Banach spaces for the following functional equation which is two types, that is, either cubic or quadratic: 2f(x+3y) + 6f(x-y) + 12f(2y) = 2f(x - 3y) + 6f(x + y) + 3f(4y). The concept of Hyers-Ulam-Rassias stability originated essentially with the Th. M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297-300.

• Honam Mathematical Journal
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• v.31 no.3
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• pp.451-462
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• 2009

In this paper we prove the superstability of a generalized exponential functional equation $f(x+y)=a^{2xy-1}g(x)f(y)$. It is a generalization of the superstability theorem for the exponential functional equation proved by Baker. Also we investigate the stability of this functional equation in the following form : ${\frac{1}{1+{\delta}}}{\leq}{\frac{f(x+y)}{a^{2xy-1}g(x)f(y)}}{\leq}1+{\delta}$.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.36-41
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• 1998

This paper presents a stabilization algorithm for a class of fuzzy systems with singleton consequect. To this aim, we introduce two canonical forms of an unforced fuzzy system and a stability theorem. A design example is shown to verify the stabilization algorithm.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.893-907
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• 2015

The Hyers-Ulam-Rassias stability of the k-th partial ternary quadratic derivations is investigated in non-Archimedean Banach ternary algebras and non-Archimedean $C^*$-ternary algebras by using the fixed point theorem.

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.313-318
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• 1994

It is well known that the neural network can be used as an universal approximater for functions and functionals. But these theoretical results are just an existence theorem and do not lead to decide the suitable network structure. This doubfulness whether a certain network can approximate a given function or not, brings about serious stability problems when it is used to identify a system. To overcome the stability problem, We suggest successive identification and control scheme with supervisory controller which always assures the identification process within a basin of attraction of one stable equilibrium point regardless of fittness of the network.

• Proceedings of the KIEE Conference
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• 1992.07a
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• pp.377-380
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• 1992

This paper proposes a novel direct adaptive pole placement control algorithm which can be applied to continuous time nonminimum phase systems. The algorithm is based on Lyapunov's direct method. By introducing an auxiliary signal, a minimal error model is constructed in state space. Using the error model an estimation law is obtained via Lyapunov's second stability theorem. The global stability of the overall system is established.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.32.5-32
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• 2001

There has been many teleoperation systems handling the micro object. However, the stability problem for these systems has not been mentioned yet. Historically, Lawrence[1] proposed the Transparency-Optimized Architecture and passivity theorem for stability analysis of bilateral teleoperation. He claimed that unless the task(or environment) impedance contains significance inertial behavior, Passivity condition for Transparency-optimized architecture is not satisfied. In this paper we propose one method which satisfies passivity condition for the micro-teleoperation system handling a insignificant inertial object and is based on the structure of Lawrence and Hashtrudi-Zaad[2] and velocity-force scaling.

• 제어로봇시스템학회:학술대회논문집
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• 1989.10a
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• pp.1091-1096
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• 1989

All mechanical systems have saturation nonlinearity in actuators or in final control elements. When controllers have integral action, reset windup can cause instability as well as make the system performance unsatisfactory. In this study, an intelligent limiter which needs no tuning of parameters is tested with the PDF controller used for control of a second order plant. This paper presents analysis of the stability of the system using the describing function method and the Nyquist stability theorem. The improvement of the system performance by the limiter is illustrated by computer simulations.

• Proceedings of the KIEE Conference
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• 2015.07a
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• pp.1339-1340
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• 2015

In this paper, we propose a low-complexity control scheme for segway. To design the controller, we use the prescribed performance function and analyze the stability of the proposed control system using the Lyapunov stability theorem. By prescribed performance function, we can adjust the transient and steady-state response. Finally, the simulation results are provided to illustrate the effectiveness of the proposed scheme.

• Journal of Institute of Control, Robotics and Systems
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• v.6 no.7
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• pp.523-528
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• 2000

In this short note the characteristics of a nonlinear system of which the state trajectories are oscillating in the phase plane are overviewed. The physical concept of stuck and sliding patch phenomena are also introduced by adding some switching functions and their stability on the sliding patches are analyzed by using the Lyapunov stability theory and Frobenius theorem.