• 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.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.331-331
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• 2000

This paper presents the mixed $H_2/H_{\infty}$ output feedback controIler design method for linear systems with delayed state. The objective is to design the output feedback controller which minimizes the H$_2$-norm of one transfer function while ensuring the H$_{\infty}$-norm of the other is held below a chosen level. When objective is tormulated in terms of a common Lyapunov function, the sufficient conditions of existence of mixed $H_2/H_{\infty}$ controller are given in terms of LMIs. terms of LMIs.

• Proceedings of the KIEE Conference
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• 1996.07b
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• pp.999-1001
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• 1996

In this paper, we represented the relation of minimum entropy/$H_{\infty}$-controller and mixed $H_2/H_{\infty}$-controller. An $H_2$ controller design problem involving a constraint on $H_{\infty}$ disturbance attenuation is considered. By the equivalence of the mixed $H_2/H_{\infty}$ control problem and the minimum entropy/$H_{\infty}$-control problem, we presented the controller state-space realization. Decentralized case was illustrated briefly.

• International Journal of Control, Automation, and Systems
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• v.6 no.1
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• pp.1-14
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• 2008

This paper presents a convex optimization method for observer-based mixed $H_2/H_{\infty}$ control design of linear systems with time-varying state, input and output delays. Delay-dependent sufficient conditions for the design of a desired observer-based control are given in terms of linear matrix inequalities (LMIs). An observer-based controller which guarantees asymptotic stability and a mixed $H_2/H_{\infty}$ performance for the closed-loop system of the linear system with time-varying delays is then developed. A Lyapunov-Krasovskii method underlies the observer-based mixed $H_2/H_{\infty}$ control design. A numerical example with simulation results illustrates the effectiveness of the methodology.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.529-534
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• 2005

In this paper, a new type of output feedback control, called a $H_2/H_{\infty}$ fnite memory control (FMC), is proposed for deterministic state space systems. Constraints such as linearity, unbiasedness property, and finite memory structure with respect to an input and an output are required in advance to design $H_2/H_{\infty}$ FMC in addition to the performance criteria in both $H_2$ and $H_{\infty}$ sense. It is shown that $H_2$, $H_{\infty}$, and mixed $H_2/H_{\infty}$ FMC design problems can be converted into convex programming problems written in terms of linear matrix inequalities (LMIs) with some linear equality constraints. Through simulation study, it is illustrated that the proposed $H_2/H_{\infty}$ FMC is more robust against uncertainties and faster in convergence than the existing $H_2/H_{\infty}$ output feedback control schemes.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.699-717
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• 2012

In this paper, we deal with the robust mixed $H_2/H_{\infty}$ guaranteed-cost control problem involving uncertain neutral stochastic distributed delay systems. More precisely, the aim of this problem is to design a robust mixed $H_2/H_{\infty}$ guaranteed-cost controller such that the close-loop system is stochastic mean-square exponentially stable, and an $H_2$ performance measure upper bound is guaranteed, for a prescribed $H_{\infty}$ attenuation level ${\gamma}$. Therefore, the fast convergence can be fulfilled and the proposed controller is more appealing in engineering practice. Based on the Lyapunov-Krasovskii functional theory, new delay-dependent sufficient criteria are proposed to guarantee the existence of a desired robust mixed $H_2/H_{\infty}$ guaranteed cost controller, which are derived in terms of linear matrix inequalities(LMIs). Furthermore, the design problem of the optimal robust mixed $H_2/H_{\infty}$ guaranteed cost controller, which minimized an $H_2$ performance measure upper bound, is transformed into a convex optimization problem with LMIs constraints. Finally, two simulation examples illustrate the design procedure and verify the expected control performance.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.22-22
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• 2000

This study investigates the use of mixed $H_2/H_{\infty}$ and $\mu$-synthesis to construct a robust controller for the benchmark problem. The model treated in the problem is a coupled three-inertia system which reflects the dynamics of mechanical vibrations. We, first adopt the mixed $H_2/H_{\infty}$ the to design a feedback controller K(s). Next, $\mu$-synthesis method is applied to the overall system to make use of structured parametric uncertainty.

• Journal of Institute of Control, Robotics and Systems
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• v.7 no.11
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• pp.896-903
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• 2001

This study investigates the use of mixed $H_2/H_{$\infty}$ and $\mu$-synthesis to construct a robust controller for the benchmark problem. The model treated in the problem is a coupled three-inertial system that reflects the dynamics of mechanical vibrations. This kind of problem requires to be satisfied the robust performance (both in the time and frequency-domain specifications). We, first, adopt the mixed $H_2/H_{$\infty}$ theory to design a feedback controller K(s). Next, $\mu$-synthesis method is applied to the overall system to make use of structured parametric uncertainty. This process permits higher levels of controller authority and reduces the conservativeness of the controller. Finally, the feedforward controller is also used to improve the transient response of the output. We confirm that all design specifications except a complementary sensitivity condition can be achieved.

• Journal of the Institute of Convergence Signal Processing
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• v.6 no.3
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• pp.148-156
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• 2005

The purpose of this paper is to propose an approach to design a robust servo controller based on the mixed $H_2/H_{\infty}$ theory, and confirm its validity by applying to a benchmark problem. First, the existing $H_{\infty}$ servo problem is modified to a structure for the mixed $H_2/H_{\infty}$ control problem by virtue of the internal model principle. By making use of proposed structure, we can divide specifications required in the robust servo system design into $H_2$ and $H_{\infty}$ performance criteria, respectively. It is shown that the proposed design approach is quite effective through an application to a three inertia benchmark problem.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.53 no.7
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• pp.483-490
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• 2004

The descriptor system model has a high ability in representing dynamical systems. It can preserve physical parameters in the coefficient matrices, and describe the dynamic part, static part, and even the improper part of the system in the same form. The design of mixed $H_{2}/H_{\infty}$ controllers for linear time-invariant descriptor systems is considered in this paper. Firstly, an $H_2$ and $H_{\infty}$ synthesis problems fur a descriptor system are presented separately in terms of linear matrix inequalities (LMIs) based on the bounded real lemma. Then, we show that 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 $H_2$ 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.