Results 151 to 160 of about 17,380,414 (202)
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1984
In this chapter we turn our attention to some vector boundary value problems which may be regarded as vector analogs of the scalar problems. However, as the reader will see, our results for vector problems are very incomplete, especially in comparison with the scalar theory.
K. W. Chang, F. A. Howes
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In this chapter we turn our attention to some vector boundary value problems which may be regarded as vector analogs of the scalar problems. However, as the reader will see, our results for vector problems are very incomplete, especially in comparison with the scalar theory.
K. W. Chang, F. A. Howes
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Dissipativity of Singularly Perturbed Lur’e Systems
IEEE Transactions on Circuits and Systems II: Express Briefs, 2019The problem of singularly perturbed Lur’e systems is investigated in this brief. Two new storage functions are constructed to explore the dynamics of both the fast and slow models, as well as their interaction more efficiently. By using the merit of the proposed storage functions, some new $\varepsilon $ -uniformly strict dissipativity criteria in
Yan-Wu Wang +3 more
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Singularly Perturbed Semilinear Systems
Studies in Applied Mathematics, 1979Solutions of a singularly perturbed vector boundary‐value problem are studied under the principal assumption that the trivial solution of the unperturbed equation is stable in certain senses. This is accomplished by constructing special invariant regions in which solutions display the kind of nonuniformity known as boundary‐layer behavior.
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Stabilization of Singularly Perturbed Fuzzy Systems
IEEE Transactions on Fuzzy Systems, 2004This paper presents some novel results for stabilizing singularly perturbed (SP) nonlinear systems with guaranteed control performance. By using Takagi-Sugeno fuzzy model, we construct the SP fuzzy (SPF) systems. The corresponding fuzzy slow and fast subsystems of the original SPF system are also obtained. Two fuzzy control designs are explored. In the
Tzuu-Hseng S. Li, Kuo-Jung Lin
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Discrete Approximations of Singularly Perturbed Systems
2007In the paper we study discrete approximations of singularly perturbed system in a finite dimensional space. When the right-hand side is almost upper semicontinuous with convex compact values and one-sided Lipschitz we show that the distance between the solution set of the original and the solution set of the discrete system is O(h1/2.
Tzanko Donchev, Vasile Lupulescu
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On parametric instability of singularly perturbed systems
Automation and Remote Control, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Anatoliy A. Martynyuk, A. S. Khoroshun
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Singularly Perturbed Systems of Volterra Equations
Journal of Applied Analysis, 2002This paper studies the behaviour of the solution \(u(t,\varepsilon)\) of the system of Volterra integral equations \[ \varepsilon u(t) = f(t) + \int_0^t A(t,s)u(s)\,ds, \quad 0 \leq t \leq T, \] as the positive parameter \(\epsilon\) tends to zero. Both \(f\) and \(A\) are continuous, and the eigenvalues of \(A(t,t)\) are supposed to be negative.
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On Invariant Manifolds in Singularly Perturbed Systems
Journal of Dynamical and Control Systems, 1999The 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., 2004When 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, 2001In 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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