In this paper we study the algebraic Riccati equation corresponding to the guaranteed cost control theory for an uncertain singularly perturbed system. The construction of the controller involves solving the full-order algebraic Riccati equation with small parameter ε. Under control-oriented assumptions, we first provide the sufficient conditions such that the full-order algebraic Riccati equat...

In this article, we analyze the stability and the associated bifurcations of several types of pulse solutions in a singularly perturbed three-component reaction–diffusion equation that has its origin as a model for gas discharge dynamics. Due to the richness and complexity of the dynamics generated by this model, it has in recent years become a paradigm model for the study of pulse interactions...

Abstract We study pattern formation in magnetic compounds near the helimagnetic/ferromagnetic transition point case of Dirichlet boundary conditions on spin field. The energy functional is a continuum approximation $$J_1-J_3$$ J 1 - 3 </...

In this article, we derive Ricker’s [22, 23] type nonlinear boundary condition for an age structured population dynamic model by using a singular perturbation. The question addressed in this paper is the convergence of the singularly perturbed system. We first obtain a finite time convergence for a fixed initial distribution. Then we focus on the convergence uniformly of the singularly perturbe...

In this paper a class of singularly perturbed system of conservation laws is considered. The partial differential equations are equipped with boundary conditions which may be studied to derive the exponential stability. Lyapunov stability technique is used to derive sufficient conditions for the exponential stability of this system. A Lyapunov function in H-norm for a singularly perturbed syste...

Ergodic control of singularly perturbed Markov chains with general state and compact action spaces is considered. A new method is given for characterization of the limit of invariant measures, for perturbed chains, when the perturbation parameter goes to zero. It is also demonstrated that the limit control principle is satisfied under natural ergodicity assumptions about controlled Markov chain...

In this paper, we describe a meshless approach to solve singularly perturbed differentialdifference equations of the second order with boundary layer at one end of the interval. In the numerical treatment for such type of problems, first we approximate the terms containing negative and positive shifts which converts it to a singularly perturbed differential equation. Next, a numerical scheme ba...

Abstract: This paper presents a new algorithm for the closed-loop H∞ control of a class of singularly perturbed nonlinear systems with an exogenous disturbance, using the successive Galerkin approximation (SGA). The singularly perturbed nonlinear system is decomposed into two subsystems of a slow-time scale and a fast-time scale in the spirit of the general theory of singular perturbation. Two ...