• Proceedings of the Korean Society of Precision Engineering Conference
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• 1992.10a
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• pp.215-219
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• 1992

This paper presents a motion coordination of two robot manipulators coordinating an object. To coordinate the object, a force/position control scheme in a mode of leaer/follower is devised. The dynamics of the object are incorporated into the dynamics of the leader arm, which yields a reduced order model of two arm system. In order to regulate interaction forces between two arm, the dynamics of the follower arm are expressed as force dynamic equations such that a novel direct forces between two arms and two different type of bounded input disturbances, boundedness and asymptotic stability results based on a proposed Lyapunov function are shown. Also, a sufficient condition for a stability robustness is derived based on the Lyapunov approach.

• Journal of Institute of Control, Robotics and Systems
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• v.2 no.3
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• pp.158-164
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• 1996

In this paper, we consider the problem of robust stability of discretd time-delay systems subjected to perturbations. Two classes of perturbations are treated. The first one is the nonlinear norm-bounded perturbation, and the second is the structured time-varying parametric perturbation. Based on the discrete-time Lyapunov stability theory, several new sufficient conditions for robust stability of the system are presented. From these conditions, we can estimate the maximum allowable bounds of the perturbations which guarantee the stability. Finally, numerical examples are given to demonstrate the effectiveness of the results.

• Journal of Institute of Control, Robotics and Systems
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• v.15 no.1
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• pp.67-71
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• 2009

This paper presents a rank-constrained linear matrix inequality (LMI) approach to the design of a multi-objective controller such as $H_2/H_{\infty}$ control. Multi-objective control is formulated as an LMI optimization problem with a nonconvex rank condition, which is imposed on the controller gain matirx not Lyapunov matrices. With this rank-constrained formulation, we can expect to reduce conservatism because we can use separate Lyapunov matrices for different control objectives. An iterative penalty method is applied to solve this rank-constrained LMI optimization problem. Numerical experiments are performed to illustrate the proposed method.

• Proceedings of the KIEE Conference
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• 1995.11a
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• pp.210-212
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• 1995

Its is proposed that a stable adaptive control system composed of a fuzzy and a compensating controller, is designed to control nonlinear systems. In fuzzy and proposed compensating controller, parameters of membership functions characterizing the linguistic terms change according to some adaptive law. The adaptive law are based on the Lyapunov systhesis approach. the closed-loop system using the adaptive control structure proposed in this paper is globally stable in the sense that the Lyapunov function decreases as time goes. the following simulation shows the results.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.279-292
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• 2011

In this paper, we consider anti-periodic solutions of the following BAM neural networks with multiple delays on time scales: $$\{{x^\Delta_i(t)=-a_i(t)e_i(x_i(t))+{\sum\limits^m_{j=1}}c_{ji}(t)f_j(y_j(t-{\tau}_{ji}))+I_i(t),\atop y^\Delta_j(t)=-b_j(t)h_j(y_j(t))+{\sum\limits^n_{i=1}}d_{ij}(t)g_i(x_i(t-{\delta}_{ij}))+J_j(t),}\$$ where i = 1, 2, ..., n,j = 1, 2, ..., m. Using some analysis skills and Lyapunov method, some sufficient conditions on the existence and exponential stability of the anti-periodic solution to the above system are established.

• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.89-102
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• 2010

This paper concerns the problem of global robust stability of a time-delay discontinuous system with a positive-defined connection matrix under polytopic-type uncertainty. In order to give the stability condition, we firstly address the existence of solution and equilibrium point based on the properties of M-matrix, Lyapunov-like approach and the theories of differential equations with discontinuous right-hand side as introduced by Filippov. Second, we give the delay-independent and delay-dependent stability condition in terms of linear matrix inequalities (LMIs), and based on Lyapunov function and the properties of the convex sets. One numerical example demonstrate the validity of the proposed criteria.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.52 no.3
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• pp.129-133
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• 2003

In this paper, we consider the robust guaranteed cost control problem for a class of uncertain neutral systems with given quadratic cost functions. The uncertainty is assumed to be norm-bounded and time-varying. The goal in this study is to design the memoryless state feedback controller such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound lot all admissible uncertainty. Some criteria for the existence of such controllers are derived based on the matrix inequality approach combined with the Lyapunov second method. A parameterized characterization of the robust guaranteed cost controllers is given in terms of the feasible solutions to the certain matrix inequalities. A numerical example is given to illustrate the proposed method.

• Proceedings of the KIEE Conference
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• 2002.07d
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• pp.2497-2499
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• 2002

This raper proposes a simple robust nonlinear controller design method based on Lyapunov stability for tracking reference welding trajectory and velocity of a three wheel welding mobile robot (WMR). Control law is obtained from Lyapunov control function to ensure asymptotical stability of the system. The effectiveness of the proposed controller is shown through simulation results.

• International Journal of Control, Automation, and Systems
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• v.6 no.2
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• pp.263-268
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• 2008

An improved linear matrix inequality (LMI) representation of delay-independent $H_2$ performance analysis is introduced for linear delay systems with delays of any size. Based on this representation we propose a new $H_2$ memoryless state feedback design. By introducing a new matrix variable, the new LMI formulation enables us to parameterize memoryles s controllers without involving the Lyapunov variables in the formulations. By using a parameter-dependent Lyapunov function, this new representation proposed here provides us the results with less conservatism.

• Proceedings of the KIEE Conference
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• 2000.07d
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• pp.2729-2731
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• 2000

In this paper, we propose an adaptive controller using RBFN(radial basis function network) for robot manipulators. The structure of the proposed controller consists of a RBFN and a fixed gain PD controller. On the basis of the Lyapunov stability theorem, we guarantee the UUB (uniformly ultimately boundedness) for the total system. And the learning law of RBFN is established by the Lyapunov method. Finally, we apply the proposed controller to tracking control for the 2 link SCARA type robot manipulator.