A class of singularly perturbed evolution systems

Stability Region of Singularly Perturbed Systems

 This paper studies the characterization of the stability boundary (the topological boundary of stability region) of nonlinear autonomous singularly perturbed dynamical systems. In particular, a relationship between the stability boundary of the singularly perturbed system and the stability boundary and stability region of the slow and fast systems is investigated. Conditions, in terms of loca...

Control of singularly perturbed hybrid stochastic systems

In this paper, we study a class of optimal stochastic control problems involving two different time scales. The fast mode of the system is represented by deterministic state equations whereas the slow mode of the system corresponds to a jump disturbance process. Under a fundamental “ergodicity” property for a class of “infinitesimal control systems” associated with the fast mode, we show that t...

Controller Design of Decentralized Singularly Perturbed Systems

Stochastic Stability of Singularly Perturbed Nonlinear Systems

The stability of a nonlinear stochastic dynamic system with singular perturbations is considered. Based on the notion of stochastic input-to-state stability and using time scale decomposition, a result of the total stability type is obtained, i.e. if the fast subsystem and the slow subsystem are both input-to-state stable with respect to disturbances, then this property continues to hold for th...

Approximation of singularly perturbed linear hyperbolic systems

This paper is concerned with systems modelled by linear singularly perturbed partial differential equations. More precisely a class of linear systems of conservation laws with a small perturbation parameter is investigated. By setting the perturbation parameter to zero, the full system leads to two subsystems, the reduced system standing for the slow dynamics and the boundary-layer system repre...