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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 J. Corless, Luigi Glielmo
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Finite-Time Fuzzy Control for Nonlinear Singularly Perturbed Systems With Input Constraints
Singularly perturbed systems have found widespread applications in practice. The existing results on singularly perturbed systems mainly focused on the Lyapunov asymptotic stability, which are unable to deal with the cases that the system states cannot ...
Wei Xing Zheng, Shengyuan Xu
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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 \(\det(A_0(t)-\lambda B(t))\equiv0\).
Starun, I. I., Shkil', M. I.
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ON THE CONTROL OF SINGULARLY PERTURBED NONLINEAR SYSTEMS
IFAC Proceedings Volumes, 1992Abstract Using the integral manifold concept, a recent systematic method to control e-perturbed nonlinear systems is here extended to a rather wide class of singularly perturbed MIMO systems. This class includes singularly perturbed systems exibiting an affine structure in the control after order reduction.
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