• The Transactions of the Korean Institute of Electrical Engineers D
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• v.51 no.11
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• pp.503-509
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• 2002

In this paper, the robust non-fragile guaranteed cost control problem is studied for a class of linear large-scale systems with uncertainties and a given quadratic cost functions. The uncertainty in the system is assumed to be norm-bounded and 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 a 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 for all admissible uncertainties and controller gain variations. 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 controllers is given in terms of the feasible solutions to a certain LMI. A numerical example is given to illustrate the proposed method.

• Transactions on Control, Automation and Systems Engineering
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• v.4 no.4
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• pp.324-329
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• 2002

In this paper, the guaranteed cost filtering design method for linear time delay systems with convex bounded uncertainties in discrete-time case is presented. The uncertain parameters are assumed to be unknown but belonging to known convex compact set of polytotype less conservative than norm bounded parameter uncertainty. The main purpose is to design a stable filter which minimizes the guaranteed cost. The sufficient condition for the existence of filter, the guaranteed cost filter design method, and the upper bound of the guaranteed cost are proposed. Since the proposed sufficient conditions are LMI(linear matrix inequality) forms in terms of all finding variables, all solutions can be obtained simultaneously by means of powerful convex programming tools with global convergence assured. Finally, a numerical example is given to check the validity of the proposed method.

• Journal of Electrical Engineering and Technology
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• v.10 no.3
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• pp.1255-1263
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• 2015

In the previous work, the authors studied the problem of robust discretization of linear time-invariant systems with polytopic uncertainties, where linear matrix inequality (LMI) conditions were developed to find an approximate discrete-time (DT) model of a continuous-time (CT) system with uncertainties in polytopic domain. The system matrices of obtained DT model preserved the polytopic structures of the original CT system. In this paper, we extend the previous approach to solve the problem of robust discretization of polytopic uncertain systems with aperiodic sampling. In contrast with the previous work, the sampling period is assumed to be unknown, time-varying, but contained within a known interval. The solution procedures are presented in terms of unidimensional optimizations subject to LMI constraints which are numerically tractable via LMI solvers. Finally, an example is given to show the validity of the proposed techniques.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.53 no.12
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• pp.655-660
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• 2004

This paper deals with the design of a fixed-structure $H_\infty$ power system stabilizer (PSS) by using an iterative linear matrix inequality (LMI) method. The fixed-structure $H_\infty$ controller is represented in terms of LMIs with a rank condition. To solve the non-convex rank-constrained LMI problem, a linear penalty function is incorporated into the objective function so that minimizing the penalized objective function subject to LMIs amounts to a convex optimization problem. With an increasing sequence of the penalty parameter, the solution of the penalized optimization problem moves towards the feasible region of the original non-convex problem. The proposed algorithm is, therefore, convergent. Numerical experiments show the practical applicability of the proposed algorithm.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.49 no.1
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• pp.26-32
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• 2000

In this paper, we consider to robust controller design problem for the linear large scale systems with the uncertainties and the time-delays. The considered time-delays are that exist in the state and the input of the subsystems and the interconnected subsystems. And the considered uncertainties are two general types that exist in the system, input and interconnected matrices. Based on the linear matrix inequality(LMI) and Lyapunov theorem, we present sufficient conditions for the existence of a controller that guarantees the asymptotic stability of systems regardless of the uncertainties and the time-delays. Also, the controller can be easily obtained by checking the feasibility of the LMI's. Finally, we show the usefulness of our results by an example.

• 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.

• Journal of Institute of Control, Robotics and Systems
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• v.12 no.6
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• pp.517-523
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• 2006

This paper is focused on a robust saturation controller for the stable linear time-invariant (LTI) system involving both actuator's saturation and structured real parameter uncertainties. Based on affine quadratic stability and multi-convexity concept, a robust saturation controller is newly proposed and the linear matrix inequality (LMI)-based sufficient existence conditions for this controller are presented. The controller suggested in this paper can analytically prescribe the lower and upper bounds of parameter uncertainties, and guarantee the closed-loop robust stability of the system in the presence of actuator's saturation. Through numerical simulations, it is confirmed that the proposed robust saturation controller is robustly stable with respect to parameter uncertainties over the prescribed range defined by the lower and upper bounds.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.3
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• pp.563-567
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• 2017

This paper deals with the depth and speed controls of a class of nonlinear large diameter unmanned underwater vehicles (LDUUVs), while maintaining its attitude. The concerned control problem can be viewed as an asymptotic stabilization of the error model in terms of its desired depth, surge speed and attitude. To tackle its nonlinearities, the linear parameter varying (LPV) model is employed. Sufficient linear matrix inequality (LMI) conditions are provided for its asymptotic stabilization. A numerical simulation is provided to demonstrate the effectiveness of the proposed design methodology.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.46 no.5
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• pp.22-28
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• 2009

In this paper, we consider the problem of $H_{\infty}$ filtering for continuous-time singular systems with multiple state-delays. The aim of designed filter is to guarantee regularity, impulse-free, asymptotic stability and $H_{\infty}$ norm bound of filtering error singular system. By establishing a finite sum inequality based on quadratic terms, a new delay-dependent BRL (bounded real lemma) for singular systems with multiple state-delays is derived. Based on the result, the existence condition of $H_{\infty}$ filter and filter design method are proposed in terms of LMI (linear matrix inequality). Finally, a numerical example is provided to show the validity of the design methods.

• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.1043-1056
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• 2008

The spanning column rank of an $m{\times}n$ matrix A over a semiring is the minimal number of columns that span all columns of A. We characterize linear operators that preserve the sets of matrix ordered pairs which satisfy multiplicative properties with respect to spanning column rank of matrices over semirings.