• The Transactions of The Korean Institute of Electrical Engineers
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• v.65 no.3
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• pp.457-462
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• 2016

In this paper, we consider the stability of time-delayed linear systems. To derive an LMI form of result, the integral inequality is essential, and Jensen's integral inequality was the best in the last two decades until Seuret's integral inequality is appeared recently. However, these two are proportional to the inverse of integration interval, so another integral inequality is needed to make it in the form of LMI. In this paper, we derive an integral inequality which is proportional to the integration interval which can be easily converted into LMI form without any other inequality. Also, it is shown that Seuret's integral inequality is a special case of our result. Next, based on this new integral inequality, we derive a stability condition in the form of LMI. Finally, we show, by well-known two examples, that our result is less conservative than the recent results.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.10
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• pp.1287-1292
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• 1999

In large-scale systems, we frequently encounter the time-delay and the uncertainty, and these should be considered in the design of controller because these are the source of the degradation of the system performance and instability of system. In this paper, we consider the robust stability of the linear large scale systems with the uncertainties and the time-delays. The considered uncertainties are both structured uncertainty and the unstructured uncertainty. Also, the considered time-delays are time-varying having finite time derivative limits. Based on the Lyapunov theorem and the linear matrix inequality(LMI) technique, we present two sufficient conditions that guarantee the robust stability of the system. The conditions are expressed as the LMI forms which can be easily checked their feasibility by using the well-known LMI control toolbox. Finally, we show by two examples that our results are less conservative than the previous results.

• Transactions on Control, Automation and Systems Engineering
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• v.1 no.2
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• pp.87-93
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• 1999

This paper proposes a systematic designs methodology for the Takagi-Sugeno (TS) model based fuzzy control systems with guaranteed stability and pre-specified transient performance for the application to a nonlinear magnetic bearing system. More significantly, in the proposed methodology , the control design problems which considers both stability and desired transient performance are reduced to the standard LMI problems . Therefore, solving these LMI constraints directly (not trial and error) leads to a fuzzy state-feedback controller such that the resulting fuzzy control system meets above two objectives. Simulation and experimentation results show that the proposed LMI-based design methodology yields only the maximized stability boundary but also the desired transient responses.

• Journal of Mechanical Science and Technology
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• v.17 no.1
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• pp.105-113
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• 2003

This paper proposes a systematic design methodology for the Takagi-Sugeno (TS) model based fuzzy state feedback control system with multi-objectives. In this investigation, the objectives are set to be guaranteed stability and pre-specified transient performance, and this scheme is applied to a nonlinear magnetic bearing system. More significantly, in the proposed methodology, the control design problems that consider both stability and desired transient performance are reduced to the standard LMI problems. Therefore, solving these LMI constraints directly (not trial and error) lead to a fuzzy state-feedback controller such that the resulting fuzzy control system meets the above two objectives. Simulation and experimentation results show that the Proposed LMI-based design methodology yields not only maximized stability boundary but also the desired transient responses.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.49 no.4
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• pp.165-174
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• 2000

This paper presents the application of H$\infty$ control synthesis using LMI optimization method to power system stabilizer(PSS) design. Since power system is usually operated under circumstance of unmeasurable uncertainties and external disturbances, the improvement of small signal stability becomes one of the most important issue for securing system stability and preventing low frequency oscillation phenomena. The LMI optimized H$\infty$ PSS provides robust performance and guarantees the internal stability under these operating conditions. The global optimal H$\infty$ norm is found using LMI convex optimization method which is more systematic than standard two Riccati solution method. The design results are simulated for a case study. We verified that the LMI method shows the best performance characteristic smong standard Riccati method and conventional lead/lag method.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.44 no.1
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• pp.57-69
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• 2016

There are three kinds of algorithms(2-ARE, mu-synthesis, LMI) for controller design using closed-loop shaping method. This paper provides the summary of background theory of three algorithms and $H_{\infty}$ controller design results for spacecraft attitude control using the three controller design tools of Matlab$^{TM}$ Toolbox for comparison. As a result, it reveals that LMI design method is more reliable as well as easier than others for spacecraft attitude control design. Comparison results are as follow: 2-ARE method and LMI method provide almost same results in robust stability, robust performance and control authority level. But 2-ARE method is more sensitive than LMI method with respect to proper design of weighting functions: 2-ARE method is more difficult than LMI method in weighting function design. The design result of mu-synthesis method shows worse performance and requires bigger control authority than others.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.12
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• pp.2480-2483
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• 2009

This paper presents an LMI-based method to design a integral sliding mode controller for a class of uncertain time-delay systems. Using LMIs we derive an existence condition of a sliding surface guaranteeing the asymptotic stability of the sliding mode dynamics. And we give a switching feedback control law. Our method is a generalization of the previous integral sliding mode control design methods. Since our method is based on LMIs, it gives design flexibility for combining various useful design criteria that can be captured in the LMI-based formulation. We also give LMI existence conditions of sliding surfaces guaranteeing a-stability or LQ performance constraint. Finally, we give a numerical design example to show the effectiveness of the proposed method.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.4
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• pp.788-792
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• 2010

The problem of delay-dependent and parameter-dependent robust stability condition for discrete-time uncertain singular systems with polytopic uncertainty and interval time-varying delay is considered. A new robust stability condition based on parameter-dependent Lyapunov function is derived in terms of LMI (linear matrix inequality). Moreover, the proposed robust stability condition is a general condition for both singular and non-singular systems. A numerical example is presented to demonstrate the effectiveness of the proposed method.

• Proceedings of the KIEE Conference
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• 2009.07a
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• pp.1727_1728
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• 2009

Nowadays DC-DC converter has been used widely in electronic production. It has a high requirement in wide input voltage, load variations, stability, providing a fast transient response and lower overshoot. However, it is not easy to be controlled because of its nonlinearity. In this paper, the nonlinear model of DC-DC converter is approximatedby four linear models and sub-controllers are designed by using the LMI guaranteeing the stability of the sub-systems at the same time. For the robust of the control system, an integral sliding mode control (ISMC) is applied together with LMI fuzzy controller. The proposed controller supports a fast and almost no overshooting transient response for the DC-DC converter control.

• Transactions of The Korea Fluid Power Systems Society
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• v.5 no.1
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• pp.1-5
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• 2008

Pneumatic driving systems have hard non-linear characteristic and large friction force compared with driving power. Hence, it cannot be robust against parameter uncertainties, modelling error, disturbance and noise. In this study, we apply a mixed $H_2/H_{\infty}$ control to the generalized plant for a pneumatic driving apparatus system including parameter uncertainty and disturbance. In order to design the $H_2/H_{\infty}$ controller, we use the LMI technique. To evaluate control performance and robust stability of the designed controller, we compare it with a conventional controller such as PVA(Position-Velocity-Acceleration state controller) using the simulation results. As a result, it can be known that designed controller shows better robust stability than the conventional controller.