• Journal of the Korean Institute of Telematics and Electronics
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• v.23 no.5
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• pp.653-657
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• 1986

This paper describes a method to design a guaranteed cost controller for a system with uncertain parameters. The design procedure consists of defining an arbitrary function which satisfies certain condition and minimizing it over the control input. When the method is applied to a class kof linear systems with uncertain parameters, a Riccati equation with additional terms results. A simple example is presented to illustrate the usefulness of this method.

• International Journal of Control, Automation, and Systems
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• v.4 no.2
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• pp.172-177
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• 2006

In the networked control system (NCS), the uncertain network-induced delay and nonlinear controlled object are the main problems, because they can degrade the performance of the control system and even destabilize it. In this paper, a class of uncertain and nonlinear networked control systems is discussed and its sufficient condition for the robust asymptotic stability is presented. Further, the maximum network-induced delay that insures the system stability is obtained. The Lyapunov and LMI theorems are employed to investigate the problem. The result of an illustrative example shows that the robust stability analysis is sufficient.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.1758-1763
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• 2004

This paper focuses on congestion control for ATM network with uncertain time-variant delays. The time-variant delays can be distinguished into two distinct components. The first one is represented by time-variant queueing delays in the intermediate switches that are occurred in the return paths of RM cells. The next one is a forward path delay. It is solved by the VBR model which quantifies the data propagation from the sources to the switch. Robust $H_8$ control is studied for solving congestion problem with norm-bounded time-varying uncertain parameters. The suitable robust $H_8$ controller is obtained from the solution of a convex optimization problem through LMI technique.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.322-326
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• 2003

In this paper, we establish a new robust $H_{\infty}$ performance condition for uncertain discrete-time systems with convex polytopic uncertainties. We express the condition as a set of linear matrix inequalities (LMIs), which are used to check stability and $H_{\infty}$ disturbance attenuation level by a parameter-dependent Lyapunov matrix. We show that the new condition provides less conservative result than the existing ones which use single Lyapunov matrix. We also show that the robust $H_{\infty}$ state feedback design problem for such uncertain discrete-time systems can be easily dealt with using the approach. The key point in this paper is to propose a kind of decoupling between the Lyapunov matrix and the system matrices in the parameter-dependent matrix inequality by introducing one new matrix variable.

• Journal of Institute of Control, Robotics and Systems
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• v.17 no.7
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• pp.625-628
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• 2011

This paper presents an LMI-based method to design an integral sliding mode controller for a class of uncertain systems with unmatched uncertainties. The uncertain system under consideration may have unmatched parameter uncertainties in the state matrix as well as in the input matrix. Using LMIs an existence condition of a sliding surface is derived. And a switching feedback control law is given. Finally, numerical examples are given to show that the proposed method can be better than the existing results for some cases.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2000.11a
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• pp.476-479
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• 2000

This paper deals with a robust pole placement method for uncertain linear systems. For all admissible uncertain parameters, a static output feedback controller is designed such that all the poles of the closed loop system are located within the prespecfied disk. It is shown that the existence of a positive definite matrix belonging to a convex set such that its inverse belongs to another convex set guarantees the existence of the output feedback gain matrix for our control problem. By a sequence of convex optimization the aforementioned matrix is obtained. A numerical example is solved in order to illustrate efficacy of our design method.

• Industrial Engineering and Management Systems
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• v.12 no.1
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• pp.30-35
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• 2013

Motivated by the emergency scheduling in a transportation network, this paper considers a transportation problem, in which, the truck times and transportation costs are assumed as uncertain variables. To meet the demand in the practical applications, two optimization objectives are considered, one is the total costs and another is the completion times. And then, a multi-objective optimization model is developed according to the situation in applications. Because there are commensurability and conflicting between the two objectives commonly, a solution does not necessarily exist that is best with respective to the two objectives. Therefore, the problem is reduced to a single objective model, which is an uncertain programming with a chance-constrain. After some analysis, its equivalent deterministic form is obtained, which is a nonlinear programming. Based on a stepwise optimization strategy, a solution method is developed to solve the problem. Finally, the computational results are provided to demonstrate the effectiveness of our model and algorithm.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.8
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• pp.1441-1443
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• 2010

This paper presents an LMI-based method to design an integral sliding mode controller for for a class of uncertain systems with mismatched unstructured uncertainties. The uncertain system under consideration may have mismatched parameter uncertainties in the state matrix as well as in the input matrix. Using LMIs we derive an existence condition of a sliding surface. And we give a switching feedback control law. Finally, we give a numerical design example in order to show that the proposed method can be better than the existing results.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.6
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• pp.1173-1178
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• 2010

In this note, a systematic design of a new robust nonlinear integral variable structure controller based on state dependent nonlinear form is presented for the control of uncertain more affine nonlinear systems with mismatched uncertainties and matched disturbance. After an affine uncertain nonlinear system is represented in the form of state dependent nonlinear system, a systematic design of a new robust nonlinear integral variable structure controller is presented. To be linear in the closed loop resultant dynamics and remove the reaching phase problems, the linear integral sliding surface is suggested. A corresponding control input is proposed to satisfy the closed loop exponential stability and the existence condition of the sliding mode on the linear integral sliding surface, which will be investigated in Theorem 1. Through a design example and simulation studies, the usefulness of the proposed controller is verified.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.9
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• pp.1754-1760
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• 2011

In this paper, a systematic design of a robust nonlinear multivariable variable structure controller based on state dependent nonlinear form is presented for the control of MIMO uncertain affine nonlinear systems with mismatched uncertainties and matched disturbance. After a MIMO uncertain affine nonlinear system is represented in the form of state dependent nonlinear system, a systematic design of a robust nonlinear variable structure controller is presented. To be linear in the closed loop resultant dynamics, the linear sliding surface is applied. A corresponding diagonalized control input is proposed to satisfy the closed loop global exponential stability and the existence condition of the sliding mode on the linear sliding surface, which will be investigated in Theorem 1. Through a design example and simulation study, the usefulness of the proposed controller is verified.