Results 161 to 170 of about 9,050,649 (204)

On Invariant Manifolds in Singularly Perturbed Systems

Journal of Dynamical and Control Systems, 1999
The author deals with a slow-fast system \[ \dot x=f(x,y, \varepsilon), \quad \dot y=\varepsilon g(x,y, \varepsilon), \quad \dot\varepsilon=0 \] where \(x\in\mathbb{R}^\ell\), \(y\in\mathbb{R}^m\), \(\varepsilon\in \mathbb{R}\). Assuming that the fast system \(\dot x=f(x,y,0)\), \(\dot y=0\) has a compact smooth invariant manifold with boundary \(M_0 ...
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Relaxation in singularly perturbed control systems

Proceedings of the 41st IEEE Conference on Decision and Control, 2002., 2004
When slow and fast motions are coupled in a singularly perturbed control system, the application of relaxed controls may be needed on several levels. There may be a need to relax the control affecting the slow and the fast motions and there may be a need to relax the fast flow itself, which serves as a control for the slowly dynamics.
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Synthesis of Linear, Singularly Perturbed Systems

Journal of Mathematical Sciences, 2001
In connection with control theory the typical problem of formation of the feedback providing prescribed characteristics of the performance and stability of a closed system is considered. A concept of exterior polynomial is introduced for a system of ordinary differential equations with small parameters.
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Interval observers design for singularly perturbed systems

53rd IEEE Conference on Decision and Control, 2014
This 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, Raissi, Tarek, Amairi, Messaoud, Aoun, Mohamed   +3 more
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On output feedback control of singularly perturbed systems

Applied Mathematics and Computation, 2010
zbMATH 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, 1992
The 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, 2006
The 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., Soares, Sérgio H. M.   +1 more
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Controlled switching in singularly perturbed systems

42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475), 2004
When 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

2016
Stability 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, Zidong Wang, Jing Xu, Yun Zou   +3 more
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On singularly perturbed quasilinear systems

Applied Mathematics and Mechanics, 1987
The 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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