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Singular Singularly Perturbed Systems
2014In this chapter we consider singularly perturbed differential systems whose degenerate equations have an isolated but not simple solution. In that case, the standard theory to establish a slow integral manifold near this solution does not work. Applying scaling transformations and using the technique of gauge functions we reduce the original singularly
Elena Shchepakina +2 more
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Discretization schemes for nonlinear singularly perturbed systems
[1991] Proceedings of the 30th IEEE Conference on Decision and Control, 2002The authors study the effect of slow and fast sampling and analyze the structure of the resulting sampled models in the case of nonlinear singularly perturbed systems. Using combinatorial equalities, related to the Baker-Campbell-Hausdorff formula, discretization schemes for such systems are proposed.
Barbot J. P. +3 more
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On the controllability of singularly perturbed systems
IEEE Transactions on Automatic Control, 1977Sufficient conditions for controllability of high-order systems of singularly perturbed type are formulated in terms of two lower order subsystems. At first, linear time-varying systems are considered and then the results are extended to a class of nonlinear systems.
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Averaging of singularly perturbed systems
Nonlinear Analysis: Theory, Methods & Applications, 1997The paper considers singularly perturbed control systems of the form \[ \dot z=f(z,y,u(t),\varepsilon), \qquad \dot y=g(x,y,u(t),\varepsilon). \] Instead of studying the algebraic differential system obtained by letting \(\varepsilon\to 0\) the author takes the averaging approach, constructing a limiting differential inclusion for the slow motion.
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On linearization of nonlinear singularity perturbed systems
IEEE Transactions on Automatic Control, 1986The linearization of nonlinear singularly perturbed systems with the help, in the first case, of corresponding map finding for systems with linear fast variables and using in the second case, the slow invariant manifold for general nonlinear singularly perturbed control systems is considered.
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The phenomenon of “breaking down” in singularly perturbed systems
Journal of Mathematical Sciences, 1996See the review in Zbl 0804.34050.
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Controlled Singularly Perturbed Systems
1990Many control problems can be modelled by systems of differential equations where the state variable can be divided into two coupled groups. Those in the first group change at a “normal” rate, and those in the second group change at a much “faster” rate.
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A novel -dependent Lyapunov function and its application to singularly perturbed systems
Automatica, 2021Wei Xing Zheng, Shengyuan Xu
exaly
Singularly Perturbed Discontinuous Systems
1992One of the major obstacles in the use of efficient tools for designing control systems is the high order of equations that describe their behaviour. In many cases they may be reduced to a lower order model by neglecting small time constants or rejecting fast components of the system overall motion.
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