• Transactions on Control, Automation and Systems Engineering
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• v.2 no.3
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• pp.163-168
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• 2000

The problems of mixed $H_2/H_{\infty}$ filtering design fer continuous and discrete time linear systems with time delay are investigated. The main purpose is to design a stable mixed $H_2/H_{\infty}$ filter which minimizes the H$_2$Performance measure satisfying a prescribed H$_{\infty}$ norm bound on the closed loop system in continuous-time case and discrete-time case, respectively. The sufficient conditions of existence of filter, the mixed $H_2/H_{\infty}$ filter design method, and the upper bound of performance measure are proposed by LMI(linear matrix inequality) techniques in terms of all finding variables. Also, we present optimization problems in order to get the optimal mixed $H_2/H_{\infty}$ filter in continuous and discrete time case, respectively.

• 제어로봇시스템학회:학술대회논문집
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• 1999.10a
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• pp.129-132
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• 1999

This paper deals with the optimal filtering problem constrained to input noise signal corrupting the measurement output for linear discrete-time systems. The transfer matrix H$_2$and/or H$_{\infty}$ norms are used as criteria in an estimation error sense. In this paper, the mixed $H_2/H_{\infty}$ filtering Problem in lineal discrete-time systems is solved using the LMI approach, yielding a compromise between the H$_2$and H$_{\infty}$ filter designs. This filter design problems we formulated in a convex optimization framework using linear matrix inequalities. A numerical example is presented.

• Proceedings of the KIEE Conference
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• 1998.07b
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• pp.750-753
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• 1998

This paper gives a simple parameterization of all stable unbiased filters to solve the suboptimal mixed $H_2/H_{\infty}$ filtering problem. Using the central filter, mixed $H_2/H_{\infty}$ filter is designed which minimizes the upper bound for the $H_2$ norm of the transfer matrix from a white noise to the estimation error subject to an $H_{\infty}$ norm constraint on the transfer matrix from an energy-bounded noise to the estimation error. The problem of finding suitable estimator gain can be converted into a convex optimization problem involving linear matrix inequalities.

• Transactions on Control, Automation and Systems Engineering
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• v.3 no.3
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• pp.139-145
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• 2001

In this paper, we consider the H$_2$(or guaranteed cost control) and H$_{\infty}$ controller design methods for singular(or descriptor) systems with input time delay. Also, a mixed H$_2$and H$_{\infty}$ controller design algorithm is treated by combination of the proposed H$_2$and H$_{\infty}$ controller design method. The sufficient conditions for the existence of controllers and controller design methods are introduced at each Lemma and Theorem. Furthermore, we present optimization problems to get the upper bound of performance measures. The proposed methods are checked by examples.