• 충청수학회지
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• 제30권2호
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• pp.273-284
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• 2017

In this paper, we study that the solutions to perturbed differential system $$y^{\prime}=f(t,y)+{{\displaystyle\smashmargin{2}{\int\nolimits_{t_0}}^{t}}g(s,y(s),T_1y(s))ds+h(t,y(t),T_2y(t))$$ have uniformly Lipschitz stability by imposing conditions on the perturbed part ${\int_{t0}^{t}}g(s,y(s),T_1y(s))ds,h(t,y(t),T_2y(t))$, and on the fundamental matrix of the unperturbed system y' = f(t, y) using integral inequalities.

• 대한수학회보
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• 제38권1호
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• pp.101-111
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• 2001

We investigate the property of h-stability, which is an important extension of the notions of exponential stability and uniform Lipschitz stability in variation for nonlinear Volterra difference systems.

• 한국산업정보학회논문지
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• 제11권5호
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• pp.62-66
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• 2006

We investigate various $\Phi(t)-stability$ of comparison differential equations and we abtain necessary and/or sufficient conditions for the uniform asymptotic and exponential asymptotic stability of the nonlinear differential equation x'=f(t, x).

• Transactions on Control, Automation and Systems Engineering
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• 제2권4호
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• pp.255-261
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• 2000

This paper presents the results of the robust H(sub)$\infty$ FIR filtering for a class of nonlinear continuous time-varying systems subject to real norm-bounded parameter uncertainty and know Lipschitz nonlinearity under sampled measurements. We address the problem of designing filters, using sampled measurements, which guarantee a prescribed H(sub)$\infty$ performance in continuous time-varying context, irrespective of the parameter uncertainty and unknown initial states. The infinite horizon causal H(sub)$\infty$FIR filter are investigated using the finite moving horizon in terms of two Riccati equations with finite discrete jumps.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제23권1호
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• pp.1-12
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• 2016

This paper shows that the solutions to the perturbed differential system $y^{\prime}=f(t, y)+\int_{to}^{t}g(s,y(s),Ty(s))ds+h(t,y(t))$ have asymptotic property and uniform Lipschitz stability. To show these properties, we impose conditions on the perturbed part $\int_{to}^{t}g(s,y(s),Ty(s))ds+h(t,y(t))$, and on the fundamental matrix of the unperturbed system y' = f(t, y).

• 호남수학학술지
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• 제30권2호
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• pp.369-378
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• 2008

Modeling nonlinear friction effects is a challenging problem. In this paper, a tracking controller is proposed for a system with uncertain nonlinear friction dynamics. Instead of using a specific friction model, we assume that the friction dynamics are represented by a function, which is unknown except its being continuously differentiable and Lipschitz continuous with known Lipschitz constants. It is shown that the scheme results in friction identification and trajectory position and velocity tracking. The analysis is done using Lyapunov-based stability method.

• 충청수학회지
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• 제28권1호
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• pp.1-12
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• 2015

We present a local convergence analysis for inexact Newton-like method in a Banach space under weaker Lipschitz condition. The convergence ball is enlarged and the estimates on the error distances are more precise under the same computational cost as in earlier studies such as [6, 7, 11, 18]. Some special cases are considered and applications for solving nonlinear systems using the Newton-arithmetic mean method are improved with the new convergence technique.

• 제어로봇시스템학회논문지
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• 제10권10호
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• pp.907-914
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• 2004

In this paper, we present a reduced-order observer for a class of nonlinear systems based on the input output linearization. While the most results in the literature presented full-order nonlinear observer, we proposed a procedure for the design of reduced-order observer far nonlinear systems that are not necessarily observable. Assuming that there exists a global observer fer internal dynamics and that certain functions are globally Lipschitz, we can design a global reduced-order observer An illustrative example is included that demonstrate the design procedure of the proposed reduced-order observer.

• 한국산업정보학회논문지
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• 제12권5호
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• pp.54-59
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• 2007

We abtain some stability results for a very general differential system using the method of cone valued vector Lyapunov functions and conversely some sufficient conditions for existence of such vector Lyapunov functions.

• 전자공학회논문지SC
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• 제49권3호
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• pp.26-30
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• 2012

본 논문에서는 출력에 시간지연이 존재하는 이산 시간 비선형 시스템에 대한 상태관측기 설계방법을 제안한다. 비선형항에 대한 Lipschitz 조건을 가정하고 비선형항을 하나의 상태변수처럼 고려함으로써 비선형 이산시간 오차동역학방정식의 안정도 문제가 시간지연을 갖는 선형방정식의 안정도 문제로 변환될 수 있음을 보인다. 또한, 시간 지연 값에 의존적인 충분조건을 선형행렬 부등식을 이용하여 제시한다. 마지막으로 제안한 결과의 유효성을 증명하기 위하여 모의실험 예제를 제공한다.