Singular perturbation problems, also known as stii, are not easily treated analytically or numerically, as the partition of the system on slow and fast subsystems in the vicinity of the singular point(s) is required. The most common analytical technique to study such problems is the method of matched asymptotic expansions which involves nding outer and inner solutions of the system and their ma...

This paper develops a unified framework for studying robustness of the input-to-state stability (ISS) property and presents new results on robustness of ISS to slowly varying parameters, to rapidly varying signals, and to generalized singular perturbations. The common feature in these problems is a time-scale separation between slow and fast variables which permits the definition of a boundary ...

Ionic channels and semiconductor devices use atomic scale structures to control macroscopic flows from one reservoir to another. The onedimensional steady-state Poisson-Nernst-Planck (PNP) system is a useful representation of these devices but experience shows that describing the reservoirs as boundary conditions is difficult. We study the PNP system for two types of ions with three regions of ...

Sufficient conditions for the existence and uniqueness, and estimates, of a continuous vector solution y = y(t) to the integral equation y(t) = u(t) + EL(t) Ef t M(s) f(s,y(s)) ds + K(t,s) f(s,y(s)) ds, t 0 are derived. A successive approximation technique involving a double sequence is used in the proof . This integral equation result is applied to the second order singular perturbation proble...

in this paper, we try to use modeling based on singular perturbation theory, in order to control satellite attitude during the wide rolling angle maneuvering through nonlinear h∞ control strategy. differential equations describing dynamics of the satellite are presented first, and by choosing the appropriate dynamic model for actuators and based on the standard singular perturbation model, the ...

Two singularly perturbed convection-diiusion-reaction equations are examined to show the eeect of small spatial inhomogeneities on metastable dynamics in one spatial dimension. The two problems that are considered are the Ginzburg-Landau equation from phase separation theory and a viscous shock problem modeling transonic nozzle ow. For each problem, the diierential operator is perturbed by an e...