• Journal of the Korean Institute of Telematics and Electronics B
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• v.33B no.5
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• pp.33-40
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• 1996

In this paper, we propose the discrete model reduction method of bounded real transfer functions. From the discrete bounded real lemma, we obtain the two riccati equations and define the disrete bounded real balancing using solutions of these two riccati equations. And we get the reduced order discrete model from the GSPA of full order model. Especially, when free parameter of GSPA is .+-.1, we show that the reduced order discrete model retains minimality, stability, and bounded real and BR-balancing properties. And we derive the .inf.-norm error bound between full order model and reduced order model. Finally to illustrate the validity of proposed method, we give an example.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.5
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• pp.615-621
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• 1999

In this paper, we consider the robust stability of uncertain linear systems with time-delay in the time domain. The considered uncertainties are both the unstructured uncertainty which is only Known its norm bound and the structured uncertainty which is known its structured. Based on Lyapunov stability theorem and{{{{ { H}_{$\infty$ } }}}} theory known as Strictly Bounded Real Lemma (SBRL), we present new conditions that guarantee the robust stability of system. Also, we extend this to multiple time-varying delays systems and large-scale systems, respectively. Finally, we show the usefulness of our results by numerical examples.

• 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.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.46 no.5
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• pp.22-28
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• 2009

In this paper, we consider the problem of $H_{\infty}$ filtering for continuous-time singular systems with multiple state-delays. The aim of designed filter is to guarantee regularity, impulse-free, asymptotic stability and $H_{\infty}$ norm bound of filtering error singular system. By establishing a finite sum inequality based on quadratic terms, a new delay-dependent BRL (bounded real lemma) for singular systems with multiple state-delays is derived. Based on the result, the existence condition of $H_{\infty}$ filter and filter design method are proposed in terms of LMI (linear matrix inequality). Finally, a numerical example is provided to show the validity of the design methods.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.48 no.5
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• pp.59-65
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• 2011

In this paper, we present a reduced-order parameter-dependent robust $H_{\infty}$ filter design method for discrete-time singular systems with polytopic uncertainties. A BRL(bounded real lemma) for parameter-dependent singular systems is derived from a parameter-dependent Lyapunov function. On the basis of the obtained BRL, low order robust $H_{\infty}$ filter design method is presented by polytopic approach, new reduced-order method, and LMI(linear matrix inequality) technique. Finally, a numerical example is presented to illustrated the feasibility of the proposed method.

• International Journal of Control, Automation, and Systems
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• v.3 no.2
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• pp.143-151
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• 2005

This paper considers a robust decentralized $H_\infty$ control problem for uncertain large-scale interconnected systems. The uncertainties are assumed to be time-invariant, norm-bounded, and exist in subsystems. A design method based on the bounded real lemma is developed for a dynamic output feedback controller, which is reduced to a feasibility problem for a nonlinear matrix inequality (NMI). It is proposed to solve the NMI iteratively by the idea of homotopy, where some of the variables are fixed alternately on each iteration to reduce the NMI to a linear matrix inequality (LMI). A decentralized controller for the nominal system is computed first by imposing structural constraints on the coefficient matrices gradually. Then, the decentralized controller is modified again gradually to cope with the uncertainties. A given example shows the efficiency of this method.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.688-691
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• 1997

This paper presents an $H^{\infty}$ controller design method for linear time-invariant systems with delayed state and control. Using the second method of Lyapunov, the stability for delayed systems is discussed. For delayed systems, we derive a sufficient condition of the bounded real lemma(BRL) which is similar to BRL for nondelayed systems. And the sufficient conditions for the existence of an output feedback $H^{\infty}$ controller of any order are given in terms of three linear matrix inequalities(LMls). Futhermore, we briefly explain how to construct such controllers from the positive definite solutions of their LMIs and give a simple example to illustrate the validity of the proposed design procedure.e.

• 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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• 2003.10a
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• pp.892-897
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• 2003

This paper considers the design of mixed $H_2/\;H_{\infty}$ controllers for linear time-invariant descriptor systems. Firstly, an $H_{\infty}$ and $H_2$ synthesis problem for a descriptor system are presented separately in terms of linear matrix inequalities (LMIs) based on the bounded real lemma. Then, the existence of a mixed $H_2/\;H_{\infty}$ controller by which the $H_2$ norm of the second channel is minimized while keeping the $H_{\infty}$ norm bound of the first channel less than ${\gamma}$, is reduced to the linear objective minimization problem. The class of desired controllers that are assumed to have the same structure as the plant is parameterized by using the linearizing change of variables. In addition, we show the procedure by which a obtained descriptor controller can be transformed to a non-descriptor one.

• Proceedings of the KIEE Conference
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• 1997.11a
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• pp.146-148
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• 1997

An LMI-based parameterization of all $\gamma$-suboptimal reduced-order unbiased $H_{\infty}$ filters is provided in terms of a free matrix, using the unbiasedness condition, bounded real lemma and the general solution of the basic LMI. Also, by sequentially solving the generalized eigenvalue minimization and basic LMI problem, the optimal filter coefficient matrix can be obtained with the best achievable performance.