• Journal of the Korean Institute of Telematics and Electronics S
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• v.34S no.10
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• pp.52-58
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• 1997

In this paper, we consider methods of robust stabilization of the interval plant with a PID controller. Suppose that we know apriori a sign of the coefficients of the numerator of the PID controller. Under this condition, it sufficies to make eight polynomials stable for robust stabilization of the interval plant with a minimum phase PID controller. In addition, with a nonminimum phase PID controller, it suffices to make different eight polynomials stable. Especially, with the nonminimum phase PID controller it is shown that stabilization of eight plants is necessary and sufficient for robust stabilization of the interval plants.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.46 no.3
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• pp.15-21
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• 2009

In this paper, we consider the design problem of robust stabilization and robust guaranteed cost state feedback controller for discrete-time singular systems with parameter uncertainties by LMI(linear matrix inequality) approach without semi-definite condition and decomposition of system matrices. The objective of robust stabilization controller is to construct a state feedback controller such that the closed-loop system is regular, causal, and stable. In the case of robust guaranteed cost control, the optimal value of guaranteed cost and controller design method are presented on the basis of robust stabilization control technique. Finally, a numerical example is provided to show the validity of the design methods.

• Journal of Institute of Control, Robotics and Systems
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• v.15 no.2
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• pp.121-127
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• 2009

This paper deals with the design problem of robust stabilization and non-fragile controller for discrete-time singular systems with parameter uncertainties and time-varying delays in state and input by delay-dependent Linear Matrix Inequality (LMI) approach. A new delay-dependent bounded real lemma for singular systems with time-varying delays is derived. Robust stabilization and robust non-fragile state feedback control laws are proposed, which guarantees that the resultant closed-loop system is regular, causal and stable in spite of time-varying delays, parameter uncertainties, and controller gain variations. A numerical example is given to show the validity of the design method.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.45 no.5
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• pp.1-7
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• 2008

This paper presents not only the robust stabilization technique but also robust non-fragile controller design method for discrete-time singular systems and static state feedback controller with multiplicative uncertainty. The condition for the existence of robust stabilization controller, the admissible controller design method, and the measure of non-fragility in controller are proposed via LMI(linear matrix inequality) approach. In order to get the maximum measure of non-fragility, the obtained sufficient condition can be rewritten as LMI optimization form in terms of transformed variable. Therefore, the presented robust non-fragile controller for discrete-time singular systems guarantees robust stability in spite of parameter uncertainty and controller fragility. Finally, a numerical example is given to show the validity of the design method.

• Proceedings of the IEEK Conference
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• 2006.06a
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• pp.947-948
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• 2006

This paper proposes a robust posture stabilization control method for wheeled mobile robots. To solve the robust posture stabilization, we introduce reference generation mode, reference tracking mode, and reference regulation mode. In reference generation mode, a kinematic time-invariant controller is used to generate the reference trajectory which starts from the initial posture of the actual robot to the desired posture. In reference tracking mode, a sliding mode position controller is employed in such a way that the actual robot can follow the reference trajectory in the desired forward or backward moving direction, even in the presence of the disturbances in the dynamics. In reference regulation mode, a sliding mode heading direction controller is used such that the actual robot can maintain the desired posture against the disturbances. In this way, robust posture stabilization can be achieved at almost all global regions.

• Proceedings of the KIEE Conference
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• 1993.07a
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• pp.328-330
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• 1993

In this paper, we present a robust $H^{\infty}$ controller for a state delayed system with uncertainties. The unstructured and norm bounded uncertainties enter into both the state and the input matrix, where the matching condition of the uncertainties is not assumed. A robust stabilization condition and also a robust $H^{\infty}$ stabilization condition are suggested. The robust $H^{\infty}$ controller is obtained by solving a Riccati equation which is derived from the suggested robust $H^{\infty}$ stabilization condition.

• International Journal of Control, Automation, and Systems
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• v.5 no.5
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• pp.594-600
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• 2007

A sufficient condition for the robust D-stability of dynamic interval systems is proposed in this paper. This D-stability condition is based on a parameter-dependent Lyapunov function obtained from the feasibility of a set of matrix inequalities defined at a series of partial-vertex-based interval matrices other than the total vertex matrices as previous results. This condition is also extended to the robust D-stabilization problem of dynamic interval systems, which supplies an effective synthesis procedure for any LMI D-region. The proposed conditions can be simplified to a set of LMIs, which can be solved by efficient interior point methods in polynomial time.

• Proceedings of the KIEE Conference
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• 1998.07b
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• pp.647-649
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• 1998

This paper describes a robust stabilization of single input nonlinear systems with parametric uncertainty. We first investigate differential flatness of the nominal nonlinear systems. If a single input system is differentially flat, it possesses a flat output. And we define coordinate transformation functions via successively differentiating the flat output, and we also consider the robust fictitious controls at every differentiation of the flat output. In the new coordinates the nonlinear system is transformed into the Brunovsky normal form with matched uncertainty. With a robust control based on the Lyapunov method, the robust stabilization is achieved.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10b
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• pp.586-591
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• 1992

In this paper a robust stabilization problem is discussed for plant with both time-varying parameter perturbations and unstructured uncertainty. It is shown that, a robust L$_{2}$-stabilizing controller can be obtained by solving an H$_{\infty}$ standard problem with a scaling parameter. Using an H$_{\infty}$ design method, a robust L$_{2}$-stabilizing controller is derived. Finally, a numerical example is given.n.

• Journal of Institute of Control, Robotics and Systems
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• v.20 no.8
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• pp.822-827
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• 2014

This paper presents a robust observer-based output feedback control for stabilization of linear time invariant systems with polytopic uncertainties. To this end, this paper not only finds a robust observer gain but also suggests how to determine the model used in the observer, which is not obvious due to model uncertainties in the conventional observer design method. The robust observer gain and the observer model are selected in a way that the whole closed-loop is stable by solving LMIs and BMIs (Linear Matrix Inequalities and Bilinear Matrix Inequalities). A simulation example shows that the proposed robust observer-based output feedback control successfully leads to closed-loop stability.