• 제어로봇시스템학회:학술대회논문집
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• 1999.10a
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• pp.88-91
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• 1999

The purpose of this paper is to propose an approach to design a robust servo controller based on the Mixed H$_2$/H$\sub$$\infty$/ theory. In order to do this, we first modify the generalized plant for the usual H$\sub$$\infty$/ servo problem to a structure of the Mixed H$_2$/H$\sub$$\infty$/ minimization problem by virtue of the internal model principle. By doing this, we can divide specifications adopted for robust servo system design into H$_2$and H$\sub$$\infty$/ performance criteria, respectively. Then, the mixed H$_2$/H$\sub$$\infty$/ problem is solved in order to find the best solution, by which we can minimize H$_2$-norm of the transfer function under the condition of H$\sub$$\infty$/-norm value, through Linear Matrix Equality (LMI).

• Journal of the Korean Institute of Intelligent Systems
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• v.22 no.4
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• pp.441-447
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• 2012

This paper presents a design technique of a Takagi-Sugeno (T-S) fuzzy-model-based $H_{\infty}$ controller for autonomous underwater vehicles (AUVs). The design procedure aims to render the stabilizing controller which satisfies performance of the diving control for AUVs in the presence of the disturbance. A nonlinear AUV is modeled by the T-S fuzzy system through the sector nonlinearity. By using Lyapunov function, the sufficient conditions are derived to guarantee the performance of robust depth control in the format of linear matrix inequality (LMI). To succeed for diving control of AUV, we add the constraints on the diving and pitch angles in the LMI conditions. Through the simulation, we confirm the effectiveness of the proposed methodology.

• Journal of the Institute of Convergence Signal Processing
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• v.3 no.2
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• pp.76-82
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• 2002

The objective of this paper is to design a robust controller for a flexible robot arm manipulator using LMI(Linear Matrix Inequality) theory, and confirm its effectiveness through experimentation. We first describe a modeling Process of the flexible arm in order to get a mathematical model, and then discuss how to approximately obtain the uncertainty of the model for robust control. As to the control system design, we adopt the LMI-based H$_{\infty}$ synthesis algorithm which has the merits of eliminating the regularity restrictions attached to the Riccati-based methods. As a result of this, we can cope with the parameter variation (that is, modeling uncertainty) due to the tip-load variation. Finally we confirm the effectiveness of the controller through experiment and simulation.

• Transactions on Control, Automation and Systems Engineering
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• v.1 no.2
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• pp.106-112
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• 1999

This paper presents an H$\infty$ controller design method for linear systems with time-varying delayed states, inputs, and measurement outputs. Using a Lyapounov unctional , the stability for delay systems is discussed independently of time delays . And a sufficient condition for the existence of H$\infty$ controllers of n-th order is given in terms of three matrix inequalities. Based on the positive-definite solutions of their matrix inequalities, we briefly explain how to construct H$\infty$ construct H$\infty$ controller, which stabilizes time-delay systems independently of delays and guarantees an H$\infty$ norm bound.

• 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.

• Journal of Institute of Control, Robotics and Systems
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• v.4 no.2
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• pp.151-156
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• 1998

This paper presents an $H_{\infty)$ output feedback controller design method for linear systems with delayed state, delayed control input, and delayed masurement output. Using a Lyapunov functional, the stability for delayed systems is discussed independently of delays. Also, sufficient condition for the existence of $H_{\infty)$ controllers of any order is given in terms of three linear matrix inequalities(LMIs). Based on positive definite solutions of their LMIs, we briefly explain the way to construct $H_{\infty)$ controller, which stabilizes time-delay systems independently of delays and guarantees an $H_{\infty)$norm bound.

• International Journal of Control, Automation, and Systems
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• v.6 no.2
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• pp.171-179
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• 2008

This paper addresses the synthesis of an iterative learning controller for a class of linear systems with norm-bounded parameter uncertainties. We take into account an iterative learning algorithm with current cycle feedback in order to achieve both robust convergence and robust stability. The synthesis problem of the developed iterative learning control (ILC) system is reformulated as the ${\gamma}$-suboptimal $H_{\infty}$ control problem via the linear fractional transformation (LFT). A sufficient convergence condition of the ILC system is presented in terms of linear matrix inequalities (LMIs). Furthermore, the ILC system with fast convergence rate is constructed using a convex optimization technique with LMI constraints. The simulation results demonstrate the effectiveness of the proposed method.

• Proceedings of the KIEE Conference
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• 1999.11c
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• pp.494-496
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• 1999

In this paper, we consider the design of a state feedback $H_{\infty}$ controller for uncertain linear systems with saturating actuators. We consider a general saturating actuator and employ the additive decomposition to deal with it effectively. And the considered uncertainty is the unstructured uncertainty which is only known its norm bound. Based on Linear Matrix Inequality(LMI) techniques, we present a condition on designing a controller that guarantees the $L_2$ gain, from the noise to the output, is not greater than a given value. A controller is obtained by checking the feasibility of three LMI's, and this can be easily done by well-known control package. Finally, we show the usefulness of our result by a numerical example.

• Proceedings of the KIEE Conference
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• 1999.07b
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• pp.596-598
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• 1999

In this paper, we consider the design of a state feedback $H_{\infty}$ controller for linear systems with saturating actuators. We consider a general saturating actuator and employ the multiplicative decomposition to deal with it effectively. Based on Linear Matrix Inequality (LMI) techniques, we present a condition on designing a controller that guarantees the $L_2$ gain, from the noise to the output, is not greater than a given value. A controller is obtained by checking the feasibility of three LMI's, and this can be easily done by well-known control package. Finally, we show the usefulness of our result by a numerical example.

• Journal of Power System Engineering
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• v.3 no.2
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• pp.84-88
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• 1999

In this paper, systems described by state-space models are considered. For these systems, author studies the decoupling of linear systems and gives a sufficient condition for a system to be made feedback decouplable. Especially, the condition is given by LMI(Linear Matrix Inequality) form. Based on this condition, it is guaranteed that the system decoupling problem is achieved and the $H_{\infty}$ constraint is satisfied simultaneously. This result can be easily extended to the robust decoupling control system design problems.