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Linearization of Hamiltonian and Gradient Systems
IMA Journal of Mathematical Control and Information, 1984Necessary and sufficient conditions are derived in order to transform a nonlinear Hamiltonian or gradient system by a change of coordinates of its state space into a linear Hamiltonian or gradient system. It is shown that such a transformaion necessarily respects the symplectic or metrical structure. The conditions are given in terms of the observation
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On the discretization of linear continuous Hamiltonian systems
2015 12th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE), 2015When you discretized a continuous time linear Hamiltonian system you may expect that the result will be a discrete time Hamiltonian system, However this is not always true. In this paper we compare the following methods: Forward Euler, Backward Euler, Pole-Zero matching and Zero-order hold, in order to see which one preserves the Hamiltonian property ...
Jose Guillermo Rodriguez Servin +1 more
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Decomposition of linear port-Hamiltonian systems
Proceedings of the 2011 American Control Conference, 2011It is well known that the power conserving interconnection of finite dimensional port-Hamiltonian systems is also a port-Hamiltonian system. Given a linear port-Hamiltonian system, this paper proposes conditions under which the control system can be expressed as a composition of two linear port-Hamiltonian systems.
K. Höffner, Martin Guay
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2009
In this chapter we study Hamiltonian systems which are linear differential equations. Many of the basic facts about Hamiltonian systems and symplectic geometry are easy to understand in this simple context. The basic linear algebra introduced in this chapter is the cornerstone of many of the later results on nonlinear systems. Some of the more advanced
Kenneth Meyer, Glen Hall, Dan Offin
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In this chapter we study Hamiltonian systems which are linear differential equations. Many of the basic facts about Hamiltonian systems and symplectic geometry are easy to understand in this simple context. The basic linear algebra introduced in this chapter is the cornerstone of many of the later results on nonlinear systems. Some of the more advanced
Kenneth Meyer, Glen Hall, Dan Offin
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GKN theory for linear Hamiltonian systems
Applied Mathematics and Computation, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhaowen Zheng, Shaozhu Chen
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Oscillation results for linear Hamiltonian systems
Applied Mathematics and Computation, 2002The author considers linear Hamiltonian systems. He uses the generalized Riccati technique and establishes some new oscillation criteria of Philos and Kamenev types. The results improve some of the well-known results in the literature. Some examples are considered to illustrate the main results.
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1990
Consider a system of m linear equations with continuous T -periodic coefficients: $$ \dot x = M\left( t \right)x $$ (1) where M (t) is a real m × m matrix, depending continuously on t ∈ ℝ such that: $$ M\left( {t + T} \right) = M\left( t \right) $$ (2) .
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Consider a system of m linear equations with continuous T -periodic coefficients: $$ \dot x = M\left( t \right)x $$ (1) where M (t) is a real m × m matrix, depending continuously on t ∈ ℝ such that: $$ M\left( {t + T} \right) = M\left( t \right) $$ (2) .
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On the Linearization of Hamiltonian Systems on Poisson Manifolds
Mathematical Notes, 2005Let \((M,\{.,.\},H)\) be a Hamilton-Poisson system. Acording to the general scheme, the linearization procedure applied to the dynamical system \((M,X_H)\) defines a vector field Var\((X_H)\) on the tangent bundle \(TM\). Let \((N,\omega)\) be a closed symplectic leaf of \((M,\{.,.\})\), \(T_{N}M\) the restriction of the tangent bundle \(TM\) to the ...
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Discrete Linear Hamiltonian Systems
1996This chapter is an introduction to Martin Bohner’s approach to the discrete linear Hamiltonian system $$\begin{array}{*{20}{c}} {\Delta y\left( t \right) = A\left( t \right)y\left( {t + 1} \right) + B\left( t \right)z\left( t \right)} \\ {\Delta z\left( t \right) = C\left( t \right)y\left( {t + 1} \right) - A*\left( t \right)z\left( t \right ...
Calvin D. Ahlbrandt, Allan C. Peterson
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Moment matching for linear port Hamiltonian systems
IEEE Conference on Decision and Control and European Control Conference, 2011The problem of moment matching with preservation of port Hamiltonian structure is tackled. Based on the time-domain approach to linear moment matching, we characterize the (subset of) port Hamiltonian models from the set of parameterized models that match the moments of a given port Hamiltonian system, at a set of finite points.
Tudor Corneliu Ionescu +1 more
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