• International Journal of Aeronautical and Space Sciences
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• v.7 no.2
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• pp.1-13
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• 2006

The Lyapunov stability theory has been known inadequate to prove capturability of guidance laws because the equations of motion resulted from the guidance laws do not have the equilibrium point. By introducing a proper transformation of the range state, the original equations of motion for a stationary target can be converted into nonlinear equations with a specified equilibrium subspace. Physically, the equilibrium subspace denotes the direction of missile velocity to the target. By using a single Lyapunov function candidate, capturability of several PN laws for a stationary target is then proved for examples. In this approach, there is no assumption of the constant speed missile. The proposed method is expected to provide a unified and simplified scheme to prove the capturability of various kinds of guidance laws.

• Proceedings of the KIEE Conference
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• 2004.07d
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• pp.2516-2518
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• 2004

This paper proposes a stability condition in discrete-time affine Takagi-Sugeno (T-S) fuzzy systems with parametric uncertainties and then, introduces the design method of a fuzzy-model-based controller which guarantees the stability. The analysis is based on Lyapunov functions that are continuous and piecewise quadratic. The search for a piecewise quadratic Lyapunov function can be represented in terms of linear matrix inequalities (LMIs).

• Earthquakes and Structures
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• v.21 no.6
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• pp.577-585
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• 2021

In this research, a neural network (NN) method was developed, which combines H-infinity and fuzzy control for the purpose of stabilization and stability analysis of nonlinear systems. The H-infinity criterion is derived from the Lyapunov fuzzy method, and it is defined as a fuzzy combination of quadratic Lyapunov functions. Based on the stability criterion, the nonlinear system is guaranteed to be stable, so it is transformed to be a linear matrix inequality (LMI) problem. Since the demo active vibration control system to the tuning of the algorithm sequence developed a controller in a manner, it could effectively improve the control performance, by reducing the wind's excitation configuration in response to increase in the cost efficiency, and the control actuator.

• Proceedings of the KIEE Conference
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• 2001.11c
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• pp.76-79
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• 2001

This paper is concerned with a stability analysis of Madam Type fuzzy systems. It Introduces the canonical form of an unforced fuzzy system and its stability theorem suggested in the previous study. Then it gives new simplified stability conditions based on the Lyapunov function method. A common positive definite matrix in the stability conditions is searched by the LMI method.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.583-596
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• 2010

In this paper, the problem of delay-dependent stability analysis for cellular neural networks systems with time-varying delays was considered. By using a new Lyapunov-Krasovskii function, delay-dependant stability conditions of the delayed cellular neural networks systems are proposed in terms of linear matrix inequalities (LMIs). Examples are provided to demonstrate the reduced conservatism of the proposed stability results.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.44 no.2 s.314
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• pp.1-9
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• 2007

In this paper, new results for perturbation bounds for unified decentralized systems by a unified approach using $\delta$ (defined as a shift operator at unified approach) are presented. Robust stability analysis of unified decentralized system is investigated by new robust stability bound under system uncertainties. New unified stability bounds are developed based on the unified Lyapunov matrix equation. It is shown that the system maintains its stability when new unified bounds are applied. Numerical example is presented to illustrate the proposed analysis.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1993.06a
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• pp.873-876
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• 1993

A fuzzy controller designed by mini-max-gravity(MMG) method is essentially nonlinear with respect to the controller's input and output relationship, and stability analysis is thus needed to construct a stable control system. This paper deals with a design method of a position-type MMG fuzzy controller stable in a sense of Lyapunov when considered is a single-input-single-output linear, stable plant. We first introduce a method to construct a Laypunov function by using an eigen-value of A matrix of the linear, stable plant dynamics and then we derive an asymtotic stability condition in terms of scale factors for fuzzy state variables and controller gain. The stability condition is found reasonably practical through comparing the theoretical stability region with that obtained from simulations.

• Journal of Power Electronics
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• v.17 no.6
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• pp.1611-1624
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• 2017

With the rapid development of microgrid technology, microgrid projects are no longer limited to laboratory demonstrations and pilot platforms. It shows greater value in practical applications. Hence, the smooth interaction between a microgrid and the main grid plays a critical role. In this paper, a control method based on active disturbance rejection control (ADRC) is proposed in order to realize seamless transitions between grid-connected and islanding operation modes and stable operation with variable loads. It is verified by simulations that the proposed ADRC-based method features better performance when compared to conventional proportional-integral-differential (PID) control. Meanwhile, the stability of the third-order extended state observer (ESO) in second-order ADRC is validated by using Lyapunov stability criteria.

• Korean Journal of Applied Biomechanics
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• v.18 no.1
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• pp.21-30
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• 2008

The purpose of this study was to investigate the variability to compare local dynamic stability via a linear and nonlinear analysis during walking. Twenty four elderly males, 12 healthy elderly and 12 patients with osteoarthritise walked on a treadmill for 100 consecutive strides. Lyapunov exponent and correlation dimension and coefficient variation were calculated for the kinematic parameters to determine the dynamic stability during walking. The linear measures indicated that the healthy elderly demonstrated significantly higher variability in the ankle joint displacement. The nonlinear analysis revealed that COD for the knee joint angle were higher in patient with osteoarthritise. There were no coincidence in results between linear and nonlinear techniques over two groups. In light of nonlinear analysis, it was concluded that patients with osteoathritise showed higher local instability during walking.

• Journal of the Korean Institute of Intelligent Systems
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• v.25 no.4
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• pp.349-354
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• 2015

This paper presents the stability conditions of the Takagi-Sugeno (T-S) fuzzy sampled-data filter. The error system between the T-S fuzzy system and fuzzy filter is presented. In the sense of the Lyapunov stability analysis, the stability conditions are given, which can be represented in terms of linear matrix inequalities (LMIs). The proposed stability conditions utilize the different approach from the conventional methods, and have better performance than that of the conventional ones. The simulation example is given to show the effectiveness of the proposed method.