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Interval observers design for singularly perturbed systems
53rd IEEE Conference on Decision and Control, 2014This paper deals with interval observers design for two-time singularly perturbed systems. The full-order system is firstly decoupled into slow and fast subsystems. Then, using the cooperativity theory, an interval observer is designed for the slow subsystem assuming that the singular perturbed parameter is uncertain.
Yousfi, Basma +3 more
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On output feedback control of singularly perturbed systems
Applied Mathematics and Computation, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
GLIELMO L, CORLESS M.
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Suboptimization of Singularly Perturbed Control Systems
SIAM Journal on Control and Optimization, 1992The singularly perturbed control system \(\dot z=f_ 1(z,y,u)\), \(z(0)=z_ 0\), \(\varepsilon\dot y=f_ 2(z,y,u)\), \(y(0)=y_ 0\), is studied and compared with the `reduced system' \(\dot z=f_ 1(z,\psi(z,u),u)\), \(z(0)=z_ 0\), where \(y=\psi(z,u)\) is the root of the static equation \(0=f_ 2(z,y,u)\). It is shown that the reduced system approximates the
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Singularly perturbed elliptic systems
Nonlinear Analysis: Theory, Methods & Applications, 2006The authors prove the existence of a family of positive solutions for two coupled nonlinear stationary Schrödinger equations, concentrating at a point in the limit. In some cases the location of the concentration point is given in terms of the potential functions of the stationary Schrödinger equations.
Alves, Claudianor O. +1 more
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Controlled switching in singularly perturbed systems
42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475), 2004When slow and fast motions are coupled in a singularly perturbed control system, abrupt changes in the fast flow may result in switching between modes in the slow dynamics. Such changes may be desirable due to design specifications or considerations of optimality.
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Stabilization of Singularly Perturbed Systems
2016Stability analysis and controller design are significant problems of dynamic systems in theory and practice that have attracted the interest of many investigators [4]. In recent decades, researchers have focused on the problem of stability analysis and stabilization for SPSs, and these approaches can improve the control precision of system.
Chenxiao Cai +3 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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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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