• The Transactions of the Korean Institute of Electrical Engineers D
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• v.55 no.4
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• pp.147-153
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• 2006

In this paper, we propose a new delay-dependent criterion on the robust stability of time-delayed linear systems having norm bounded uncertainties. Based on new form of Lyapunov-Krasovskii functional and the Newton-Leibniz formula, we drive a result in the form of LMI which guarantees the robust stability without any model transformation. The Newton-Leibniz equation was used to relate the cross terms with free matrices. Finally, we show the usefulness of our result by two numerical examples.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.25-25
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• 2000

This paper presents a design method of sliding mode control (SMC) for single input linear systems with mismatched uncertainties. We define a virtual state based on the controllable canonical form of the nominal system. And we define a sliding surface for the augmented system with a virtual state. This sliding surface makes it possible to use SMC technique with various types of controllers. In this paper, we construct a controller that combines SMC with robust controller. We design a robust controller for the system with only mismatched uncertainties using a form of linear matrix inequality (LMI). We make a virtual state from this robust control input and the states of the nominal system. And we design a sliding mode controller that stabilizes the overall closed-loop system.

• Journal of Institute of Control, Robotics and Systems
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• v.7 no.3
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• pp.193-197
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• 2001

This paper presents a design method of sliding model control (SMC) for single input linear systems with mismatched uncertainties. We define a virtual state based on the controllable canonical form of the nominal system. And we defined a sliding surface for the augmented system with a virtual state. This sliding surface makes it possible to use the SMC technique with various types of controllers. In this paper, we construct a controller that combines SMC with robust controller. We design a robust controller for the system with mismatched uncertainties using a form of linear matrix inequality(LMI). We make a virtual state from this robust control input and the states of the nominal system. And we design a sliding model controller that stabilizes the overall closed-loop system.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.49 no.4
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• pp.191-200
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• 2000

In practical applications, we frequently encounter the actuator nonlinearity in control systems, and its representative nonlinearity is saturation. A controller designed without considering this saturation nonlinearity is often a source of degradation of performance. To treat the saturation nonlinearity more efficiently, we adopt the multiplicative decomposition and the additive decomposition. Based on these decompositions, we present two controller design methods in the LMI(Linear Matrix Inequality) form that guarantee the L2 gain, from the disturbance to the measured output, is less than or equal to a given value. Finally, we give two examples to show the applicability and usefulness of our results.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.41 no.3
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• pp.9-16
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• 2004

This paper provides an observer-based Η$\infty$ output feedback controller design method for descriptor systems with time-varying delay by just one LMI(linear matrix inequality) condition. The sufficient condition for the existence of controller and the controller design method are presented by perfect LMI approach which can be solved efficiently by convex optimization. The design procedure involves solving an LMI. Since the obtained condition can be expressed as an LMI form all variables including feedback gain and observer gain can be calculated simultaneously by Schur complement changes of variables, and singular value decomposition. Moreover, The proposed controller design algorithm can be extended to the observer-based robust Η$\infty$ output feedback controller design method for descriptor systems with parameter uncertainty and time delay. An example is given to illustrate the results.

• Journal of information and communication convergence engineering
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• v.6 no.2
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• pp.198-203
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• 2008

An Intelligent optimal control system design algorithm in active suspension equipment adopting linear matrix inequalities control system design theory with representing by descriptor system form is presented. The validity of the linear matrix inequalities intelligent decentralized control system design with representing by descriptor system form in active suspension system through the numerical examples is also investigated.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.40 no.3
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• pp.99-108
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• 2003

This paper is concerned with the problem of designing a guaranteed cost state feedback controller for singular systems with time-varying delays. The sufficient condition for the existence of guaranteed cost controller, the controller design method, and the optimization problem to get the upper bound of guaranteed cost function are proposed by LMI(linear matrix inequality), singular value decomposition, Schur complements, and change of variables. Since the obtained sufficient conditions can be changed to LMI form, all solutions including controller gain and the upper bound of guaranteed cost function can be obtained simultaneously. Moreover, the proposed controller design method can be extended to the problem of robust guaranteed cost controller design method for singular systems with parameter uncertainties and time-varying delays. The validity of the proposed design algorithm is investigated through a numerical example.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.8
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• pp.1464-1470
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• 2010

In this paper, we consider the $H_{\infty}$ control of time-delayed linear systems with saturating actuators. The considered time-delay is a time-varying one having bounds on magnitude and time-derivative, and the control permits the predetermined degree of saturation. Based on two modified Lyapunov-Krasovskii(L-K) functionals, we derive a $H_{\infty}$ control in the form of linear matrix inequalities(LMI) having three non-convex design parameters. The result is dependent on the characteristics of time-delay, predetermined degree of saturation level, and bound of disturbance. Finally, we give a comparative example to show the effectiveness and usefulness of our result.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.9
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• pp.1748-1753
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• 2011

In this paper, we consider the stability of linear systems with an interval time-varying delay. It is known that the adoption of decomposition of delay improves the stability result. For the interval time-delay case, they applied it to the interval of time-delay and got less conservative results. Our basic idea is to apply the general decomposition to the low limit of delay as well as interval of time-delay. Based on this idea, by using the modified Lyapunov-Krasovskii functional and newly derived Lemma, we present a less conservative stability criterion expressed as in the form of linear matrix inequality(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
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• v.62 no.5
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• pp.673-678
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• 2013

This paper considers the stability of linear systems having an interval time-varying delay using a switched system approach. The time-delay system is converted to the switched system equivalently, and then a stability criterion in the form of linear matrix inequality(LMI) is derived by using a parameter dependent Lyapunov-Krosovskii function(PD-LKF). In constructing a PD-LKF, the decomposition is employed for delay free intervals, and the reduction of conservatism is shown analytically as the number of decomposition increases. Finally, two well-known numerical examples are given to show the reduction of conservatism compared to the recent results.