• International Journal of Control, Automation, and Systems
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• v.4 no.6
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• pp.697-704
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• 2006

The paper is concerned with $H_{\infty}$ filtering for descriptor systems. A necessary and sufficient condition is established in terms of linear matrix inequalities(LMIs) for the existence of normal filters such that the error systems are admissible and the transfer function from the disturbance to the filtering error output satisfies a prescribed $H_{\infty}$-norm bound constraint. When these LMIs are feasible, an explicit parameterization expression of all desired normal filter is given. All these results are yielded without decomposing the original descriptor systems, which makes the filter design procedure simple and direct. Finally, a numerical example is derived to demonstrate the applicability of the proposed approach.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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• pp.48-51
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• 1996

This note considers the $H^{\infty}$ controller design problem for linear systems with time-varying delays in states. We obtain sufficient conditions for the existence of k-th order $H^{\infty}$ controllers in terms of three linear matrix ineualities(LMIs). These sufficient conditions are dependent on the maximum value of the time derivative of time-varying delay. Furthermore, we briefly explain how to construct such controllers from the positive definite solutions of their LMIs and give an example.e.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.109-112
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• 1997

In this note, we investigate a noniterative design method of an observer-based robust H$\_$2/ controller in the presence of structured real parameter uncertainty by applying Riccati approach based on the guaranteed cost function. Motivated by the numerical difficulty of the problem, we try to develop a simple design method named as block-diagonal approach, which can be solved by the LMIs method. By assuming the block-diagonal structure of Riccati solution, the original problem can be derived into two sequentially decoupled optimization problems as LQG control problem. The proposed method seems to be numerically efficient in obtaining a feasible compensator.

• Journal of Institute of Control, Robotics and Systems
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• v.3 no.2
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• pp.109-114
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• 1997

In this paper, we present an output feedback $H^\infty$controller design method and derive the sufficient condition of the bounded real lemma for linear systems with multiple delays in states. For state delayed systems, sufficient conditions for the existence $\kappa$-th order $H^\infty$controllers are given in terms of three linear matrix inequalities(LMIs). Furthermore, we show how to construct such controllers from the positive definite solutions of their LMIs and given an example to illustrate the validitiy of the proosed design procedure.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.1072-1077
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• 2004

This paper provides a new approach to analyze the stability of a general multi-link TCP Vegas, which is a kind of feedback-based congestion algorithm. Whereas the conventional approaches use the approximately linearized model of the TCP Vegas along equilibrium pints, this approach models a multi-link TCP Vegas network in the form of a piecewise linear multiple time-delay system. And then, based on the exactly characterized dynamic model, this paper presents a new stability criterion via a piecewise and multiple delay-dependent Lyapunov-Krasovskii function. Especially, the resulting stability criterion is formulated in terms of linear matrix inequalities (LMIs).

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.2430-2434
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• 2003

This paper provides a new approach to analyze the stability of TCP Vegas, which is a kind of feedback-based congestion control algorithm. Whereas the conventional approaches use the approximately linearized model of the TCP Vegas along equilibrium points, this approach uses the exactly characterized dynamic model to get a new stability criterion via a piecewise and delay-dependent Lyapunov-Krasovskii function. Especially, the resulting stability criterion is formulated in terms of linear matrix inequalities (LMIs). Using the new criterion, this paper shows that the current TCP Vegas algorithm is stable in the sufficiently wide region of network delay and link capacity.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.903-908
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• 2003

In this paper, we present an observer-based robust controller which achieves not only robust stability but also an performance robustness for linear uncertain discrete-time systems. The performance robustness means that comparing the transient behavior of the uncertain system with a desired one generated by the nominal system, the deterioration of control performance (i.e. the error between the real response and the desired one) is suppressed without excessive control input. The control law consists of a state feedback law for the nominal system and a compensation input given by a feedback form of an estimated error signal. In this paper, we show that conditions for the existence of the observer-based controller are given in terms of linear matrix inequalities (LMIs). Finally, a numerical example is given to illustrate the proposed technique.

• Proceedings of the KIEE Conference
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• 2004.11c
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• pp.729-731
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• 2004

This paper deals with the design of a low order $H_{\infty}$ controller by using an iterative linear matrix inequality (LMI) method. The low order $H_{\infty}$ controller is represented in terms of LMIs with a rank condition. To solve the non-convex rank-constrained LMI problem, a linear penalty function is incorporated into the objective function so that minimizing the penalized objective function subject to LMIs amounts to a convex optimization problem. With an increasing sequence of the penalty parameter, the solution of the penalized optimization problem moves towards the feasible region of the original non-convex problem. The proposed algorithm is, therefore, convergent. Numerical experiments show the effectiveness of the proposed algorithm.

• Journal of Electrical Engineering and Technology
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• v.10 no.6
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• pp.2427-2433
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• 2015

This paper presents an observer-based robust controller for constant reference tracking of linear time invariant systems with polytopic model uncertainties. To this end, this paper not only designs a robust integral controller gain but also suggests how to determine the robust observer gain and the observer model used in the observer. Since the observer model selection is not obvious due to the polytopic uncertainties, particular attention needs to be paid to that. This paper computes the robust controller and observer gains first. Then, the observer model is selected in a way that the whole closedloop is stable and LMIs are used in the middle of choosing the gains and observer model. Simulation examples show that the proposed observer-based feedback control successfully achieves robust reference tracking.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.62 no.5
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• pp.679-687
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• 2013

This paper proposes a new condition about delay-dependent robust $H_{\infty}$ control of uncertain linear systems with time-varying delay and randomly occurring disturbances. The norm bounded uncertainties are subjected to the system matrices. Based on Lyapunov stability theory, a sufficient condition for designing a controller gain such that the closed-loop systems are asymptotically stable with $H_{\infty}$ disturbance level ${\gamma}$ is formulated in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are included to show the effectiveness of the presented method.