Jiing-Dong Hwang

Stability analysis of fuzzy large-scale systems

This paper is concerned with the stability problem of fuzzy large-scale systems. Each of them consists of J interconnected subsystems which are represented by Takagi-Sugeno fuzzy models. A stability criterion in terms of Lyapunovs direct method is proposed to guarantee the asymptotic stability of fuzzy large-scale systems. Finally, an example is given to demonstrate the results.

Stabilization of Nonlinear Singularly Perturbed Multiple Time-Delay Systems by Dither

Dither is a high frequency signal injected into nonlinear systems for the purpose of improving their performance. Stability of the dithered nonlinear singularly perturbed multiple time-delay reduced-order model and by using the relaxed method to analyze stability of the dithered reduced-order model when the frequency of dither is sufficient high. Moreover, if the singular perturbation parameter is sufficiently small, then stability of the relaxed model would imply stability in finite time of the dithered nonlinear singularly perturbed multiple time-delay system.

Stability analysis of neural-network interconnected systems

This paper is concerned with the stability problem of a neural-network (NN) interconnected system which consists of a set of NN models. First, a linear difference inclusion (LDI) state-space representation is established for the dynamics of each NN model. Subsequently, based on the LDI state-space representation, a stability criterion in terms of Lyapunovs direct method is derived to guarantee the asymptotic stability of NN interconnected systems. Finally, a numerical example with simulations is given to demonstrate the results.

D-stability analysis for discrete uncertain time-delay systems☆

Abstract Two cases of the robust D -stability criterion are derived for discrete uncertain systems with multiple time delays. One is a direct test and the other is a boundary test. These cases provide the sufficient conditions under which all solutions of the characteristic equation remain inside the specific disk D ( α , r ) in the presence of parametric uncertainties.

Decentralized stabilization of fuzzy large-scale systems

A stability criterion in terms of Lyapunovs direct method is derived to guarantee the asymptotic stability of fuzzy large-scale systems. Based on this criterion and the decentralized control scheme, a set of fuzzy controllers is synthesized via the technique of parallel distributed compensation to stabilize a fuzzy large-scale system which consists of a few interconnected subsystems represented by Takagi-Sugeno fuzzy models. Finally, a numerical example with simulations is given to illustrate the results.

D-stability problem of discrete singularly perturbed systems

The D-stability problem of discrete time-delay singularly perturbed systems is examined. A two-stage method is first developed to analyse the stability relationship between a discrete time-delay singularly perturbed system and its corresponding slow and fast subsystems. Finally, the upper bound of a singular perturbation parameter is derived such that D-stability of the slow and fast subsystems can imply that of the original system, provided that the singular perturbation parameter is within this bound. This fact enables us to investigate the D-stability of the original system by establishing that of its corresponding slow and fast subsystems.

Dither in linear systems with memoryless nonlinearity and optimal control

The injection of a high-frequency signal, commonly called dither, into a nonlinear system may improve its performance. Stability of the dithered system is related to that of its corresponding model - the smoothed system, of which the nonlinear element N/sub s/ (smoothed nonlinearity) is the convolution of the dither distribution and the original nonlinearity N. The dither amplitude, but not its frequency affects the sector of N/sub s/. The importance of dither frequency is found in its effect on the deviation of the smoothed system from the dithered system, and the deviation can be improved as dither frequency increases. The dither with a sufficiently high frequency may result in the smoothed systems output and the dithered systems output as close as desired. An optimal controller and a dither, as an auxiliary of the controller, are simultaneously introduced to make the stability more robust, no matter whether the controlled plant is stable or not. The main characteristic of this paper is that an algorithm is proposed to find a lower bound on dither amplitude to stabilize the nonlinear feedback system.

Stability analysis of dithered nonlinear singularly perturbed systems with time delays

A dither is a high frequency signal introduced into a nonlinear singular perturbed system, containing multiple noncommensurate time delays, in order to improve its performance. Stability of nonlinear singularly perturbed delay systems with a dither is analyzed by deriving its dithered reduced-order model and using the relaxed method to analyze stability of the dithered reduced-order model when the frequency of dither is high-enough. Moreover, stability of the relaxed model would imply stability in finite time of the dithered nonlinear singularly perturbed delay systems, provided the singular perturbation parameter is sufficiently small.<<ETX>>

Stability analysis of uncertain feedback systems with multiple time delays and series nonlinearities

Abstract In this paper, both delay-independent and delay-dependent criteria are derived to guarantee the robust stability of uncertain multiple non-commensurate time-delay systems with a class of series nonlinearities. The properties of matrix measure and Comparison theorem are employed to investigate the robust stability conditions which assure asymptotic stability rather than ultimate boundedness of trajectories.

Taming chaotic systems with dithers

Abstract A simple approach is proposed to tame chaos by injecting high-frequency signals, commonly called dithers, into the chaotic systems. Based on the relaxed method, an appropriate dither is introduced to suppress chaotic motion. If the frequency of dither is high enough, the trajectory described by the dithered chaotic system and the trajectory of its corresponding mathematical model — the relaxed system would be made as close as desired. This fact enables us to get a rigorous prediction of the dithered chaotic system’s behavior by obtaining the behavior of the relaxed system. Finally, an example with simulations is given to illustrate the concepts discussed throughout this paper.