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3 International Journal of Applied Mathematics and Computer Science

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Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays

Zhang Q., Yang L., Liao D.

International Journal of Applied Mathematics and Computer Science

2011

Vol. 21, no 4

649-658

Fuzzy cellular neural networks with time-varying delays are considered. Some sufficient conditions for the existence and exponential stability of periodic solutions are obtained by using the continuation theorem based on the coincidence degree and the differential inequality technique. The sufficient conditions are easy to use in pattern recognition and automatic control. Finally, an example is given to show the feasibility and effectiveness of our methods.

Extended Lie algebraic stability analysis for switched systems with continuous-time and discrete–time subsystems

Zhai G., Xu X., Lin H., Liu D.

International Journal of Applied Mathematics and Computer Science

2007

Vol. 17, no 4

447-454

We analyze stability for switched systems which are composed of both continuous-time and discrete-time subsystems. By considering a Lie algebra generated by all subsystem matrices, we show that if all subsystems are Hurwitz/Schur stable and this Lie algebra is solvable, then there is a common quadratic Lyapunov function for all subsystems and thus the switched system is exponentially stable under arbitrary switching. When not all subsystems are stable and the same Lie algebra is solvable, we show that there is a common quadratic Lyapunov-like function for all subsystems and the switched system is exponentially stable under a dwell time scheme. Two numerical examples are provided to demonstrate the result.

A variable structure observer for the control of robot manipulators

Abdessameud A., Khelfi M. F.

International Journal of Applied Mathematics and Computer Science

2006

Vol. 16, no 2

189-196

This paper deals with the application of a variable structure observer developed for a class of nonlinear systems to solve the trajectory tracking problem for rigid robot manipulators. The analyzed approach to observer design proposes a simple design methodology for systems having completely observable linear parts and bounded nonlinearities and/or uncertainties. This observer is basically the conventional Luenberger observer with an additional switching term that is used to guarantee robustness against modeling errors and system uncertainties. To solve the tracking problem, we use a control law developed for robot manipulators in the full information case. The closed loop system is shown to be globally asymptotically stable based on Lyapunov arguments. Simulation results on a 3-DOF robot manipulator show the asymptotic convergence of the vectors of observation and tracking errors.