• Transactions on Control, Automation and Systems Engineering
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• v.4 no.3
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• pp.199-204
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• 2002

This paper is concerned with H$_{\infty}$ controller design methods for descriptor systems with and without time-varying delays in state and control input. The sufficient condition for the existence of an H$_{\infty}$ controller and the controller design method are presented by linear matrix inequality (LMI), singular value decomposition, Schur complements, and changes of variables. Since the obtained sufficient condition can be changed to an LMI form by proper manipulations, all solutions including controller gain can be obtained at the same time. Moreover, it is shown that robust H$_{\infty}$ controller design problem for parameter uncertain descriptor systems with time-varying delays in state and control input can be solvable using the proposed method.

• Journal of Institute of Control, Robotics and Systems
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• v.19 no.3
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• pp.183-189
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• 2013

This paper presents a stabilization method for NCS (Networked Control Systems) with two additive time-varying delays. Each time delay component between the plant and the controller has different characteristics depending on communication network, and has the upper and lower bounds. The time delay occurring from the controller to the plant has an effect on the time delay occurring from the plant to the controller, and the relationship between two delays is taken into account on the stability analysis. Based on the two additive delay components and the bound conditions, the appropriate Lyapunov-Krasovskii functional and the LMI (Linear Matrix Inequality) method derive the stability condition and the $H_{\infty}$ norm constraint for time-varying delayed NCS. Simulation results are finally given to demonstrate the effectiveness of the proposed method.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.61-76
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• 2002

The robust non-fragile guaranteed cost control problem is studied in this paper for class of uncertain linear large-scale systems with time-varying delays in subsystem interconnections and given quadratic cost functions. The uncertainty in the system is assumed to be norm-hounded arid time-varying. Also, the state-feedback gains for subsystems of the large-scale system are assumed to have norm-bounded controller gain variations. The problem is to design state feedback control laws such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound far all admissible uncertainties. Sufficient conditions for the existence of such controllers are derived based on the linear matrix inequality (LMI) approach combined with the Lyapunov method. A parameterized characterization of the robust non-fragile guaranteed cost contrellers is 7iven in terms of the feasible solution to a certain LMI. Finally, in order to show the application of the proposed method, a numerical example is included.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.1
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• pp.193-198
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• 2009

In this paper, we consider the design problem of delay-dependent robust $H{\infty}$ controller of discrete-time descriptor systems with parameter uncertainties and interval time-varying delays in state and control input by delay-dependent LMI (linear matrix inequality) technique. A new delay-dependent bounded real lemma for discrete-time descriptor systems with time-varying delays is derived. The condition for the existence of robust $H{\infty}$ controller and the robust $H{\infty}$ state feedback control law are proposed by LMI approach. A numerical example is demonstrated to show the validity of the design method.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.12
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• pp.2284-2291
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• 2010

In this paper, improved stability criteria for linear systems with time-varying delays are proposed. By constructing a new Lyapunov functional, novel stability criteria are established in terms of linear matrix inequalities (LMIs). Two numerical examples are carried out to support the effectiveness of the proposed method.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.11
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• pp.2261-2265
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• 2009

In this paper, the problem of delay-dependent stability of uncertain stochastic systems with time-varying delay is considered. The uncertainties are assumed to be norm-bounded. Based on the Lyapunov stability theory, new delay-dependent stability criteria for the system are derived in terms of LMI(linear matrix inequality). Two numerical examples are given to show the effectiveness of proposed method.

• Industrial Engineering and Management Systems
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• v.9 no.3
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• pp.262-274
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• 2010

This article investigates how to adaptively predict the time-varying metrology delay that could realistically occur in the semiconductor manufacturing practice. Metrology delays pose a great challenge for the existing run-to-run (R2R) controllers, driving the process output significantly away from target if not adequately predicted. First, the expected asymptotic double exponentially weighted moving average (DEWMA) control output, by using the EWMA and recursive least squares (RLS) prediction methods, is derived. It has been found that the relationships between the expected control output and target in both estimation methods are parallel, and six cases are addressed. Within the context of time-varying metrology delay, this paper presents a modified recursive least squares-linear trend (RLS-LT) controller, in combination with runs test. Simulated single input-single output (SISO) R2R processes subject to various time-varying metrology delay scenarios are used as a testbed to evaluate the proposed algorithms. The simulation results indicate that the modified RLS-LT controller can yield the process output more accurately on target with smaller mean squared error (MSE) than the original RLSLT controller that only deals with constant metrology delays.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.10
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• pp.1854-1860
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• 2008

In this paper, we deal with the problem of delay-dependent robust and non-fragile stabilization for descriptor systems with parameter uncertainties and time-varying delays on the basis of strict LMI(linear matrix inequality) technique. Also, the considering controller is composed of multiplicative uncertainty. The delay-dependent robust and non-fragile stability criterion without semi-definite condition and decomposition of system matrices is obtained. Based on the criterion, the problem is solved via state feedback controller, which guarantees that the resultant closed-loop system is regular, impulse free and stable in spite of all admissible parameter uncertainties, time-varying delays, and controller fragility. Numerical examples are presented to demonstrate the effectiveness of the proposed method.

• 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.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.39 no.2
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• pp.95-103
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• 2002

This paper deals with the H$_{\infty}$ control problems for discrete-time linear systems with time-varying delays in states. The existence condition and the design method of the H$_{\infty}$ state feedback controller are given. In this paper, the H$_{\infty}$ control law is assumed to be a memoryless state feedback, and the upper-bound of time-varying delay and S-procedure are used. Through some changes of variables and Schur complement, the obtained sufficient condition can be rewritten as an LMI(linear matrix inequality) form in terms of all variables.