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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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Extremum-Seeking in Singularly Perturbed Hybrid Systems
IEEE Transactions on Automatic Control, 2017This technical note considers the stability of a class of singularly perturbed hybrid systems with a continuous slow subsystem. This type of system encompasses many slowly-varying adaptation schemes, such as extremum-seeking, acting on hybrid systems, such as urban traffic control and switching control.
Ronny J. Kutadinata +2 more
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On singularly perturbed quasilinear systems
Applied Mathematics and Mechanics, 1987The objective is to give sufficient conditions for the existence of solutions of a nonlinear two-point boundary value problem. We employ these results to consider the boundary layer phenomena of the quasilinear weakly coupled singularly perturbed system \[ \epsilon y''=F(t,y)y'+g(t,y)\quad (a\leq t\leq b),\quad y(a,\epsilon)=A,\quad y(b,\epsilon)=B. \]
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Natural observers for singularly perturbed mechanical systems
Proceedings of the 2005, American Control Conference, 2005., 2005In this note, we consider vector second order mechanical systems having fast sensor dynamics, and the objective is to obtain accurate estimates of the unmeasurable slow system state variables that are generated by an appropriately designed model-based observer.
Michael A. Demetriou, Nikolaos Kazantzis
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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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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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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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A novel ε-dependent Lyapunov function and its application to singularly perturbed systems
Automatica, 2021Wei Xing Zheng +2 more
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