Kyun-Sang Park

Stability Analysis of Nonstandard Nonlinear Singularly Perturbed Discrete Systems

In this brief, we consider the stability problem of nonstandard nonlinear singularly perturbed discrete systems (NN-SPDSs). Specifically, an NN-SPDS is decomposed into two standard nonlinear SPDSs. Based on the lower order subsystems of the standard nonlinear SPDSs, we analyze the stability of the NN-SPDS.

Time-scale separation of nonlinear singularly perturbed discrete systems

In this paper, we investigate the time-scale decomposition of the nonlinear singularly perturbed discrete system into lower-order subsystems; the slow subsystem and fast subsystems. In the singular perturbation method, the time-scale separation is inevitable for the analysis of the system stability and the composite control design. Using Tikhonovs theorem, we obtain the slow subsystem and the fast subsystem separated from the nonlinear singularly perturbed discrete system. This time-scale separation method plays an important role in the stability analysis, composite control design of the nonlinear singularly perturbed discrete system.

Exponential stability of singularly perturbed systems with time delay and uncertainties

Recently, there are several studies on singularly perturbed systems with time delay and uncertainties. However, the existing results show only the limited results on either time delay or uncertainties. For time delay, small time delay or time delay only on the slow state are considered while, for uncertainties, the uncertain linear singularly perturbed system or the uncertain nonlinear singularly perturbed system with the conservative condition on uncertainties are considered. In this paper, the exponential stability of singularly perturbed systems with both time delay and uncertainties is investigated in the general form.

Wheel slip control for ABS with time delay input using feedback linearization and adaptive sliding mode control

The anti-lock braking system is an important subsystem in the brake system. Using the quarter car model, we derive the dynamic system model considering the time delay on the brake torque input. A nonlinear controller with full state feedback is proposed to maintain the wheel slip ratio at the desired slip ratio. Since, in practice, we cannot measure all the state variables, we introduce an output feedback controller utilizing the nonlinear sliding observer. The nonlinear controller with the sliding observer exhibits better performance compared with the conventional controller considering no time delay input.

Robust stability of non-standard nonlinear singularly perturbed discrete systems with uncertainties

In the past several decades, the singularly perturbed discrete systems have received much attention for the stability analysis and controller design. Recently, there are some results about the nonlinear singularly perturbed discrete systems. Compared with the existing result, we consider the robust stability of the uncertain nonlinear singularly perturbed discrete systems with the less conservative assumption via the Lyapunov function method. Moreover, the previous results of the singularly perturbed discrete system are only applied to the system, which is composed of the slow part and the fast part, separately. However, we consider the non-standard nonlinear singularly perturbed discrete system in which the slow part and the fast part coexist, that is, a general case of the nonlinear singularly perturbed discrete systems. Then, by using the lower-order subsystems from two standard systems, we present the robust stability of the non-standard nonlinear singularly perturbed discrete system with uncertainties.