• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.1
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• pp.31-35
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• 1999

In this paper, we consider the robust pole assignment and the upper bound of quadratic cost function for the linear systems with time-varying uncertainy. The considered uncertainties are both the norm bounded unstructured case and the structured case that has the matrix polytope type uncertain structure. We derve conditions that guarantee the robust pole assignment inside a disk in the L.H.P. and the robust stability. Also, we derive the upper bound of quadratic cost for thil pole assigned systems. Finally, we show the usefulness of our results by an example.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.8
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• pp.1429-1433
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• 2008

In this paper, we consider the design method of robust guaranteed cost controller for discrete-time singular systems with norm-bounded time-varying parameter uncertainty. In order to get the optimum(minimum) value of guaranteed cost, an optimization problem is given by linear matrix inequality (LMI) approach. The sufficient condition for the existence of controller and the upper bound of guaranteed cost function are proposed in terms of strict LMIs without decompositions of system matrices. Numerical examples are provided to show the validity of the presented method.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.41 no.3
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• pp.79-90
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• 2004

Systematical robust stability analysis and design scheme for the feedback linearization control systems via fuzzy modeling are proposed. It is considered that uncertainty and disturbances are included in the Takagi-Sugeno fuzzy models representing the nonlinear plants. Robust stability of the closed system is analyzed by casting the systems into the diagonal norm bounded linear differential inclusions and by converting the analysis and design problems into the linear matrix inequality optimization, a numerical method for finding the maximum stable ranges of the fuzzy feedback linearization control gains is also proposed. To verify the effectiveness of the proposed scheme, the robust stability analysis and control design examples are given.

• International Journal of Control, Automation, and Systems
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• v.4 no.4
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• pp.448-455
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• 2006

This paper deals with the observer design problem for a class of state-delayed nonlinear systems with or without time-varying norm-bounded parameter uncertainty. The nonlinearities under consideration are assumed to satisfy the global Lipschitz conditions and appear in both the state and measured output equations. The problem we address is the design of a nonlinear observer such that the resulting error system is globally asymptotically stable. For the case when there is no parameter uncertainty, a sufficient condition for the solvability of this problem is derived in terms of linear matrix inequalities and the explicit formula of a desired observer is given. Based on this, the robust observer design problem for the case when parameter uncertainties appear is considered and the solvability condition is also given. Both of the solvability conditions obtained in this paper are delay-dependent. A numerical example is provided to demonstrate the applicability of the proposed approach.

• International Journal of Control, Automation, and Systems
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• v.3 no.2
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• pp.225-235
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• 2005

This paper presents the robust stability analysis and design methodology of the fuzzy feedback linearization control systems. Uncertainty and disturbances with known bounds are assumed to be included in the Takagi-Sugeno (TS) fuzzy models representing the nonlinear plants. $L_2$ robust stability of the closed system is analyzed by casting the systems into the diagonal norm bounded linear differential inclusions (DNLDI) formulation. Based on the linear matrix inequality (LMI) optimization programming, a numerical method for finding the maximum stable ranges of the fuzzy feedback linearization control gains is also proposed. To verify the effectiveness of the proposed scheme, the robust stability analysis and control design examples are given.

• International Journal of Control, Automation, and Systems
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• v.3 no.2
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• pp.195-201
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• 2005

This paper discusses the problem of positive real control for uncertain 2-D linear discrete time singular Roesser models (2-D SRM) with time-invariant norm-bounded parameter uncertainty. The purpose of this study is to design a state feedback controller such that the resulting closed-loop system is acceptable, jump modes free and stable, and achieves the extended strictly positive realness for all admissible uncertainties. A version of positive real lemma for the 2-D SRM is given in terms of linear matrix inequalities (LMIs). Based on the lemma, a sufficient condition for the solvability of the positive real control problem is derived in terms of bilinear matrix inequalities (BMIs) and an iterative procedure for solving the BMIs is proposed.

• International Journal of Control, Automation, and Systems
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• v.6 no.5
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• pp.785-791
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• 2008

This paper considers the problem of robust $H_{\infty}$ control for uncertain 2-D discrete systems in the General Model via output feedback controllers. The parameter uncertainty is assumed to be norm-bounded. The purpose is the design of output feedback controllers such that the closed-loop system is stable while satisfying a prescribed $H_{\infty}$ performance level. In terms of a linear matrix inequality, a sufficient condition for the solvability of the problem is obtained, and an explicit expression of desired output feedback controllers is given. An example is provided to demonstrate the application of the proposed method.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.55 no.4
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• pp.147-153
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• 2006

In this paper, we propose a new delay-dependent criterion on the robust stability of time-delayed linear systems having norm bounded uncertainties. Based on new form of Lyapunov-Krasovskii functional and the Newton-Leibniz formula, we drive a result in the form of LMI which guarantees the robust stability without any model transformation. The Newton-Leibniz equation was used to relate the cross terms with free matrices. Finally, we show the usefulness of our result by two numerical examples.

• Proceedings of the KIEE Conference
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• 2004.07d
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• pp.2152-2154
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• 2004

A robust bending frequency tracker is proposed to design the adaptive notch filter which removes the time-varying missile structural mode from the sensor measurements. To design the bending frequency tracker, firstly, the signal model is derived from the input-output relationship of Nehorai notch filter structure. Also, the time-varying nature of the bending frequency is modelled as the norm-bounded uncertainty. Based on the uncertain signal model, it is shown that the design problem of robust bending frequency tracker can be casted into that of adaptive robust $H_{\infty}$ filter or equivalently robust LMS filter.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.62.4-62
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• 2001

In this paper, we propose a delay-dependent guaranteed cost controller design method for uncertain linear systems with time delay. The uncertainty is norm bounded and time-varying. A quadratic cost function is considered as the performance measure for the given system. Based on the Lyapunov method, sufficient condition, which guarantees that the closed-loop system is asymptotically stable and the upper bound value of the closed-loop cost function is not more than a specied one, is derived in terms of Linear Matrix Inequalities(LMIs) that can be solved sufficiently. A convex optimization problem can be formulated to design a guaranteed cost controller, which minimizes the upper bound value of the cost function. Numerical examples show the activeness of the proposed method.