• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.29-40
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• 2016

In this paper, we consider the nonlinear hyperbolic equations with forcing term. Some suffcient conditions for the oscillation are derived by using integral averaging method and a generalized Riccati technique.

• Journal of Institute of Control, Robotics and Systems
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• v.11 no.1
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• pp.13-18
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• 2005

This paper considers a design problem of the repetitive control system for linear systems with time-varying norm bounded uncertainties. Using the Lyapunov functional for time-delay systems, a sufficient condition ensuring robust stability of the repetitive control system is derived in terms of an algebraic Riccati inequality (ARI) or a linear matrix inequality (LMI). Based on the derived condition, we show that the repetitive controller design problem can be reformulated as an optimization problem with an LMI constraint on the free parameter.

• Kyungpook Mathematical Journal
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• v.49 no.4
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• pp.595-603
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• 2009

We show that for an algebraic Riccati equation $X^*B^{-1}X-T^*X-X^*T=C$, its solutions are given by X = W + BT for some solution W of $X^*B^{-1}X$ = $C+T^*BT$. To generalize this, we give an equivalent condition for $\(\array{B&W\\W*&A}\)\;{\geq}\;0$ for given positive operators B and A, by which it can be regarded as Riccati inequality $X^*B^{-1}X{\leq}A$. As an application, the harmonic mean B ! C is explicitly written even if B and C are noninvertible.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.113-116
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• 1997

In this paper, we present a robust $H^{\infty}$ controller design method for parameter uncertain time-varying systems with disturbance and that have time-varying delays in both state and control. It is found that the problem shares the same formulation with the $H^{\infty}$ control problem for systems without uncertainty. Through a certain differential Riccati inequality approach, a class of stabilizing continuous controller is proposed. For parameter uncertainties, disturbance and time varying delays, proposed controllers the plant and guarantee an $H^{\infty}$ norm bound constraint on disturbance attenuation for all admissible uncertainties. Finally a numerical example is given to demonstrate the validity of the results.ts.

• Transactions on Control, Automation and Systems Engineering
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• v.4 no.2
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• pp.140-146
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• 2002

We consider a class of large-scale interconnected time delay systems and investigate a decentralized robust passive control problem. sufficient conditions for unforced interconnected uncertain systems with time delay to be robustly stable with extended strictly passivity is given in terms of algebraic Riccati inequality and linear matrix inequality. The decentralized robust passive control problem for norm-bounded and positive real uncertainty is shown to be converted to extended strictly positive real control problem for a modified system which contains neither time delay nor uncertainty.

• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.287-290
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• 1995

Recently H$_{\infty}$ control theory for nonlinear systems based on the Hamilton-Jacobi inequality has been developed. In this paper, we apply the state feedback controller solved via Riccati equation to a semi-active suspension model, two degree of freedom vehicle model, and show that it is effective for vibration control..

• 제어로봇시스템학회:학술대회논문집
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• 1986.10a
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• pp.356-361
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• 1986

This paper presents robustness properties of LQ regulators for input-delayed systems. Using frequency-domain representations, the Kalman inequality concerning the return-difference matrix is derived. The stability margins of LQ regulators are investigated using the Kalman inequality when the open-loop system is stable. In order to obtain stability margins a upper bound of the solution of LQ Riccati equations is derived. Finally, the LQG/LTR method to improve the robustness of LQG regulators is obtained and illustrated with an example.

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.354-358
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• 1994

This study is concerned with H$_{\infty}$ control theory of nonlinear systems. Recently H$_{\infty}$ control theory has been developed to nonlinear systems, and especially nonlinear H$_{\infty}$ control theory based on the Hamilton-Jacobi inequality has been proposed. This corresponds to linear H$_{\infty}$ control theory based on the Riccati equation. In this paper, we apply it to a semi-active dynamic vibration absorber for multi-degree-of-freedom structure, and we design its state feedback controller via the Riccati equation. In the simulation, we show that it is effective for a vibration control.rol.

• 제어로봇시스템학회:학술대회논문집
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• 1998.10a
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• pp.151-156
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• 1998

In this paper, we present new control method for robot manipulators. The design objective can be the implementation of minimax controller with H$_{\infty}$ performance via LMI approach to guarantee the robustness and to obtain the exact tracking performance for robot manipulators with system parameter uncertainty and exogenous disturbance. We show that the Algebraic Riccati equation (ARE) which is needed for the construction of H$_{\infty}$ controller can be recast into the Algebraic Riccati Inequality (ARI) and the optimal control gain can be obtained by convex optimization method. Then, we will apply the proposed controller to rigid robot manipulators for verifying the performance of our controller.

• Journal of Institute of Control, Robotics and Systems
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• v.16 no.2
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• pp.140-144
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• 2010

In the case of a linear time-varying system, it is difficult to apply the conventional stability conditions of RHC (Receding Horizon Control) to real physical systems because of computational complexity comes from time-varying system and backward Riccati equation. Therefore, in this study, a frozen time RHC for a linear discrete time-varying system is proposed. Since the proposed control law is obtained by time-invariant Riccati equation solved by forward iterations at each control time, its stability can be ensured by matrix inequality condition and the stability condition based on horizon for a time-invariant system, and they can be applied to real physical systems effectively in comparison with the conventional RHC.