• International Journal of Control, Automation, and Systems
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• v.6 no.2
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• pp.288-294
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• 2008

Motivated by the fact that upper solution bounds for the continuous Lyapunov equation are valid under some very restrictive conditions, an attempt is made to extend the set of Hurwitz matrices for which such bounds are applicable. It is shown that the matrix set for which solution bounds are available is only a subset of another stable matrices set. This helps to loosen the validity restriction. The new bounds are illustrated by examples.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.46 no.4
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• pp.49-57
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• 2009

In this paper we consider the specific types of the generalized continuous-time Lyapunov equation and the existence of solution. This is motivated to analyze the system stability in situations where descriptor system has infinite eigenvalue. As main results, firstly the necessary and sufficient condition for stability of the descriptor system with index one or two will be proposed. Secondly, for the general case of any index, the similar condition for stability of descriptor system will be proposed with the specific type of the generalized Lyapunov equation. Finally some examples are used to show the validity of proposed methods.

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

• International Journal of Control, Automation, and Systems
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• v.2 no.4
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• pp.516-522
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• 2004

In this paper we investigate the properties of a generalized impulse response Gramian. The recursive relationship satisfied by the family of Gramians is established. It is shown that the generalized impulse response Gramian contains information on the characteristic polynomial of a linear time-invariant continuous system. The results are applied to model reduction problem.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2001.05a
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• pp.144-147
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• 2001

This paper presents adaptive fuzzy controller which is uncertainty or unknown variation in different parameters with nonlinear system of helicopter. The proposed adaptive fuzzy controller applied TSK(Takagi-Sugeno-Kang) fuzzy system which is not only low number of fuzzy rule, and a linear input-output equation with a constant term, but also can represent a large class of nonlinear system with good accuracy. The adaptive law was designed by using Lyapunov stability theory. The adaptive fuzzy controller is a model reference adaptive controller which can adjust the parameter $\theta$ so that the plant output tracks the reference model output. First of all, system of helicopter was considered as stopping state, and design of controller was simulated from dynamics equation with stopping state. Results show that it is controlled more successfully with a model reference adaptive controller than with a non-adaptive fuzzy controller when there is a modelling error between system and model or a continuous added noise in such unstable system.