• 대한수학회지
• /
• 제34권1호
• /
• pp.195-211
• /
• 1997

The purpose of this paper is to present the uniform asymptotic stability theorem and the uniform boundedness and uniform ultimate boundedness theorem for functional differential equations.

• Korean Journal of Mathematics
• /
• 제4권1호
• /
• pp.1-5
• /
• 1996

A strong Banach-Mackey property is established for ${\kappa}$-spaces including all complete and some non-complete metric linear spaces and some non-metrizable locally convex spaces. As applications of this result, a strong uniform boundedness result and a new Banach-Steinhaus type theorem are obtained.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1996년도 Proceedings of the Korea Automatic Control Conference, 11th (KACC); Pohang, Korea; 24-26 Oct. 1996
• /
• pp.119-122
• /
• 1996

The recently proposed control method using a Lyapunov-like function can give global asymptotic stability to a system with mismatched uncertainties if the uncertainties are bounded by a known function and the uncontrolled system is locally and asymptotically stable. In this paper, we modify the method so that it can be applied to a system not satisfying the latter condition without deteriorating qualitative performance. The assured stability in this case is uniform ultimate boundedness which is as useful as global asymptotic stability in the sense that it is global and the bound can be taken arbitrarily small. By the proposed control law we can deal with both matched and mismatched uncertain systems. The above facts conclude that Lyapunov-like control method is superior to any other Lyapunov direct methods in its applicability to uncertain systems.

• 전자공학회논문지S
• /
• 제35S권7호
• /
• pp.29-36
• /
• 1998

In this paper we propose a control law using a Lyapunov-like function that makes stable the systems which have mis-matched uncertainties. The existing control law using a Lyapunov-like function, which gives global saymptotic stability, is designed under the assumption of a targetsystem to be stable locally. But we broaden here the class of target systems by designing the control law which can give uniform ultimate boundedness to even the systems not satisfing the locally asymptotic stability. And we also show that the control law giving global asymptotic stability can be designed more systematically through using the uniform ultimate boundedness.

• 대한수학회논문집
• /
• 제19권1호
• /
• pp.113-117
• /
• 2004

A deranged Cantor set (without the uniform bounded-ness condition away from zero of contraction ratios) whose weak local dimensions for all points coincide has its Hausdorff dimension of the same value of weak local dimension. We will show it using an energy theory instead of Frostman's density lemma which was used for the case of the deranged Cantor set with the uniform boundedness condition of contraction ratios. In the end, we will give an example of such a deranged Cantor set.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1986년도 한국자동제어학술회의논문집; 한국과학기술대학, 충남; 17-18 Oct. 1986
• /
• pp.68-72
• /
• 1986

Upper bounds of the perturbed Co-semigroups of the infinite dimensional systems are investigated by using the algebraic Riccati equation(ARE). In the case that the solution P of the ARE is strictly positive, the perturbed semigroups are uniformly bounded. A sufficient condition for the solution P to be strictly positive is provided. The uniform boundedness plays an important role in extending approximately weak stability to weak stability on th whole space. Exponential Stability of the perturbed semigroups is studied by using the Young's inequlity. Some further discussions on the uniform boundedness of the perturbed semigroups are given.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 1991년도 하계학술대회 논문집
• /
• pp.678-681
• /
• 1991

In this paper, we propose a robust linear time-invariant feedback compensator design methodology for multivariable system which have both matched and mismatched uncertainties. In order to attack the problem of designing robust compensators guaranteeing uniform ultimate boundedness of every closed-loop system response within an arbitrarily small ball centered at the zero state based solely on the knowledge of the upper norm-bounds of uncertainties, we use an approach based upon the comparison theorem which is an effective approach in studying augmented feedback control systems with both mismatched and matched uncertainties. Through the approach, we draw some sufficient conditions for robust stability, and we give a simple example.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 1992년도 하계학술대회 논문집 A
• /
• pp.347-350
• /
• 1992

In this note, we propose a method for designing a robot controller which can suppress the effects of both the model uncertainty and noisy velocity measurements. The controller is an output feedback compensator of which the constant gains are given in terms of a Riccati equation and a Lyapunov equation. The controller guarantees not only uniform boundedness but uniform ultimate boundedness. The stability result is local but the region can be arbitrarily enlarged at the expense of large control gain. The control law needs neither the exact knowledge of the physical robot parameters nor clean velocity measurements.

• 한국정밀공학회지
• /
• 제30권12호
• /
• pp.1287-1293
• /
• 2013

In this paper, we consider variable speed wind turbine systems containing uncertain elements. Though PI controller is generally used for pitch control, it cannot guarantee a stability and performance of the complicated wind turbine systems. A robust pitch control scheme is proposed to regulate the electric power output above the rated wind speed. The pitch controller is designed in order to guarantee uniform boundedness and uniform ultimate boundedness based on the bound values of the set where the uncertainties are laid or moves. In order to verify the proposed control scheme, we present stability analysis and simulation results using Matlab/Simulink.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제22권1호
• /
• pp.75-90
• /
• 2015

In this paper the existence of global solutions of the parabolic cross-diffusion systems with cooperative reactions is obtained under certain conditions. The uniform boundedness of $W_{1,2}$ norms of the local maximal solution is obtained by using interpolation inequalities and comparison results on differential inequalities.