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On the Exponential Stability of Singularly Perturbed Systems
SIAM Journal on Control and Optimization, 1992For singularly perturbed systems \(\dot x=f(t,x,z,\mu)\), \(\mu\dot z=g(t,x,z,\mu)\), \textit{A. Saberi} and \textit{H. Khalil} [IEEE Trans. Autom. Control AC--29, 542-550 (1984; Zbl 0538.93049)] have shown that if both the reduced-order system \((\mu=0)\) and the boundary-layer system are exponentially stable, then also the full-order system is stable
Martin Corless, Luigi Glielmo
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Linear Singularly Perturbed Systems
Ukrainian Mathematical Journal, 2002This paper deals with singularly perturbed linear systems of the form \[ \epsilon B(t)\dot x=(A_0(t)+\epsilon A_1(t))x. \] The case is studied where the matrix pencil \(A_0(t)-\lambda B(t)\) is singular so that \(\det B(t)\equiv0\) and \(\det(A_0(t)-\lambda B(t))\equiv0\).
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