• The Transactions of the Korean Institute of Electrical Engineers
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• v.43 no.4
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• pp.648-657
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• 1994

This paper presents a solution of the H$\infty$ control problem for a linear singularly perturbed system. A sufficient condition for a linear singularly perturbed system to achieve the prescribed disturbance attenuation level is obtained. Based upon this sufficient condition, an H$\infty$ controller design method which involves the solutions of two generalized algebraic Riccati equations(GRE) is developed.

• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.407-426
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• 1997

We consider a system of perturbed linear differential equation x' =A(t)x + f(t,x) and obtain conditions to ensure the strong-equiasymptotic stability of the zero solution.

• Journal of Institute of Control, Robotics and Systems
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• v.14 no.12
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• pp.1270-1277
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• 2008

A Haar wavelet based numerical method for solving singularly perturbed linear time invariant system is presented in this paper. The reduced pure slow and pure fast subsystems are obtained by decoupling the singularly perturbed system and differential matrix equations are converted into algebraic Sylvester matrix equations via Haar wavelet technique. The operational matrix of integration and its inverse matrix are utilized to reduce the computational time to the solution of algebraic matrix equations. Finally a numerical example is given to demonstrate the validity and applicability of the proposed method.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.6
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• pp.840-847
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• 2009

This paper deals with an $H_{\infty}$ output feedback controller design for uncertain singularly perturbed T-S fuzzy systems. Integral quadratic constraints are used to describe various kinds of uncertainties of the plant. It is shown that the $H_{\infty}$ norm of the uncertain singularly perturbed fuzzy system is less than $\gamma$ for a sufficiently small $\varepsilon$ > 0 if the $H_{\infty}$ norms of both the slow and fast subsystem are less than $\gamma$. Using this fact, we develop a linear matrix inequality based design method which is independent of the singular perturbation parameter $\varepsilon$. A numerical example is provided to demonstrate the efficacy of the proposed design method.

• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.432-435
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• 1995

In this paper a new approach to obtain the solution of the linear-quadratic Gaussian control problem for singularly perturbed discrete-time stochastic systems is proposed. The alogorithm proposed is based on exploring the previous results that the exact solution of the global discrete algebraic Riccati equations is found in terms of the reduced-order pure-slow and pure-fast nonsymmetric continuous-time algebraic Riccati equations and, in addition, the optimal global Kalman filter is decomposed into pure-slow and pure-fast local optimal filters both driven by the system measurements and the system optimal control input. It is shown that the optimal linear-quadratic Gaussian control problem for singularly perturbed linear discrete systems takes the complete decomposition and parallelism between pure-slow and pure-fast filters and controllers.

• Journal of the Korean Mathematical Society
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• v.51 no.1
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• pp.99-111
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• 2014

In this paper, we deal with the problem of practical observer design and the practical stabilization for a class of perturbed impulsive systems. We show that, under the classical conditions of uniform complete controllability and uniform complete observability of the nominal system without impulsive effects, it is possible to design an observer controller for a class of perturbed linear impulsive system when the origin is not an equilibrium point.

• International Journal of Computer Science & Network Security
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• v.21 no.12
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• pp.223-227
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• 2021

A treatment based on the algebraic operations on fuzzy numbers is used to replace the fuzzy problem into an equivalent crisp one. The finite difference technique is used to replace the continuous boundary value problem (BVP) of arbitrary order 1<α≤2, with fuzzy boundary parameters into an equivalent crisp (algebraic or differential) system. Three numerical examples with different behaviors are considered to illustrate the treatment of the singular perturbed case with different fractional orders of the BVP (α=1.8, α=1.9) as well as the classical second order (α=2). The calculated fuzzy solutions are compared with the crisp solutions of the singular perturbed BVP using triangular membership function (r-cut representation in parametric form) for different values of the singular perturbed parameter (ε=0.8, ε=0.9, ε=1.0). Results are illustrated graphically for the different values of the included parameters.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.445-451
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• 2003

In this paper we study asymptotic equivalence between linear differential system x' = A(t)x and its perturbed system y' = A(t)y(y) + g(t).

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.3
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• pp.316-323
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• 2004

This paper deals with an $H_{\infty}$ output feedback controller design for singularly perturbed T-S fuzzy systems. It is shown that the $H_{\infty}$ norm of the singularly perturbed T-S fuzzy system is less than ${\gamma}$ for a sufficiently small ${\varepsilon}$>0 if the $H_{\infty}$ norms of both the slow and fast subsystem are less than ${\gamma}$. Using this fact, we develop a linear matrix inequality based design method which is independent of the singular perturbation parameter ${\varepsilon}$. A numerical example is provided to demonstrate the efficacy of the proposed design method.

• Journal of Mechanical Science and Technology
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• v.20 no.5
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• pp.591-601
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• 2006

In this paper, we present a new control methodology for perturbed crane systems. Nonlinear crane systems are transformed to linear models by feedback linearization. An inverse dynamic equation is applied to compute the system PD control force. The PD control parameters are selected based on a nominal model and are therefore suboptimal for a perturbed system. To achieve the desired performance despite model perturbations, we construct a neural network auxiliary controller to compensate for modeling errors and disturbances. The overall control input is the sum of the nominal PD control and the neural auxiliary control. The neural network is iteratively trained with a perturbed system until acceptable performance is attained. We apply the proposed control scheme to 2- and 3-degree-of-freedom (D.O.F.) crane systems, with known bounds on the payload mass. The effectiveness of the control approach is numerically demonstrated through computer simulation experiments.