• 제어로봇시스템학회:학술대회논문집
• /
• 2000.10a
• /
• pp.12-12
• /
• 2000

This paper consider a new weighted model reduction using block diagonal solutions of Lyapunov inequalities. With the input and/or output weighting function, the stability of reduced order system is quaranteed and a priori error bound is proposed. to achieve this, after finding the solutions of two Lyapunov inequalities and balancing the full order system, we find the reduced order systems using the direct truncation and the singular perturbation approximation. The proposed method is compared with other existing methods using numerical example.

• Journal of Institute of Control, Robotics and Systems
• /
• v.7 no.6
• /
• pp.465-470
• /
• 2001

This paper considers a new weighed model reduction method using block diagonal solutions of Lyapunov inequalities. With the input and/or output weighting function, the stability of the reduced order system is guaranteed and an a priori error bound is proposed. to achieve this after finding the solutions of two Lyapunov inequalities and balancing the full order system, we find the reduced order systems using the direct truncation and the singular perturbation approximation. The proposed method is compared with other existing methods using numerical examples.

• The Pure and Applied Mathematics
• /
• v.21 no.1
• /
• pp.61-75
• /
• 2014

The purpose of this paper is to obtain some integral inequalities with impulses by using the method of Stieltjes derivatives, and we use our results in the study of Lyapunov stability of solutions of a certain nonlinear impulsive integro-differential equation.

• The Pure and Applied Mathematics
• /
• v.18 no.4
• /
• pp.329-336
• /
• 2011

Some new Lyapunov-type inequalities for a class of nonlinear differential systems, which are natural refinements and generalizations of the well-known Lyapunov inequality for linear second order differential equations, are given. The results of this paper cover some previous results on this topic.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.56 no.9
• /
• pp.1648-1654
• /
• 2007

In this paper, we consider the design of $H_\infty$ high-gain state feedback control for time-delayed linear systems with limited actuator capacities. The high-gain control means that the control permits the predetermined degree of saturation. Based on new Lyapunov-Krasovskii functional, we derive a result in the form of matrix inequalities. The matrix inequalities are consisted of LMIs those confirm the positive definiteness of Lyapunov- Krasovskii functional, satisfaction of predetermined degree of saturation, reachable set and $L_2$ gain constraint. The result is dependent on the bound of time-delay and its rate, predetermined degree of saturation, actuator capacity, and the allowed size of disturbances. Finally, we give a numerical example to show the effectiveness and usefulness of our result.

• Proceedings of the KIEE Conference
• /
• 2004.07d
• /
• pp.2516-2518
• /
• 2004

This paper proposes a stability condition in discrete-time affine Takagi-Sugeno (T-S) fuzzy systems with parametric uncertainties and then, introduces the design method of a fuzzy-model-based controller which guarantees the stability. The analysis is based on Lyapunov functions that are continuous and piecewise quadratic. The search for a piecewise quadratic Lyapunov function can be represented in terms of linear matrix inequalities (LMIs).

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.66 no.1
• /
• pp.127-136
• /
• 2017

This paper investigates improved stability and stabilization criteria for sampled-data control systems. By using a suitable and newly constructed augmented Lyapunov-Krasovskii functional and some recent mathematic techniques such as auxiliary function-based integral inequalities, sufficient conditions for stability and stabilization conditions are derived within the framework of linear matrix inequalities(LMI) form. The superiority and validity of the proposed results are illustrated by three numerical examples.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.12 no.3
• /
• pp.187-192
• /
• 2012

This paper is concerned with stabilization problem of continuous-time Takagi-Sugeno fuzzy systems. To do this, the stabilization problem is investigated based on the new fuzzy Lyapunov functions (NFLFs). The NFLFs depend on not only the fuzzy weighting functions but also their first-time derivatives. The stabilization conditions are derived in terms of linear matrix inequalities (LMIs) which can be solved easily by the Matlab LMI Toolbox. Simulation examples are given to illustrate the effectiveness of this method.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.61 no.10
• /
• pp.1508-1512
• /
• 2012

This paper presents a relaxed stability condition for continuous-time affine fuzzy system using fuzzy Lyapunov function. In the previous studies, stability conditions for the affine fuzzy system based on quadratic Lyapunov function have a conservativeness. The stability condition is considered by using the fuzzy Lyapunov function, which has membership functions in the traditional Lyapunov function. Based on Lyapunov-stability theory, the stability condition for affine fuzzy system is derived and represented to linear matrix inequalities(LMIs). And slack matrix is added to stability condition for the relaxed stability condition. Finally, simulation example is given to illustrate the merits of the proposed method.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2004.04a
• /
• pp.133-136
• /
• 2004

This paper proposes a stability condition in affine Takagi-Sugeno (T-S) fuzzy systems with parametric uncertainties and then, introduces the design method of a fuzzy-model-based controller which guarantees the stability. The analysis is based on Lyapunov functions that are continuous and piecewise quadratic. The search for a piecewise quadratic Lyapunov function can be represented in terms of linear matrix inequalities (LMIs).