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Controllability of structured polynomial systems
IEEE Transactions on Automatic Control, 1999Summary: Two algorithms, based on the Gröbner basis method, which facilitate the controllability analysis for a class of polynomial systems are presented. We combine these algorithms with some recent results on output dead-beat controllability in order to obtain sufficient, as well as necessary, conditions for complete and state dead-beat ...
Nešić, D, Mareels, IMY
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The 22nd IEEE Conference on Decision and Control, 1983
In this paper we consider polynomial differential systems controlled by means of constant vector fields. We focus on systems described by homogenous polynomial vector fields whose degree of homogeneity is odd. We completely characterise the controllability properties of such systems in a manner identical to the corresponding theory of linear systems.
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In this paper we consider polynomial differential systems controlled by means of constant vector fields. We focus on systems described by homogenous polynomial vector fields whose degree of homogeneity is odd. We completely characterise the controllability properties of such systems in a manner identical to the corresponding theory of linear systems.
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Stability of switched polynomial systems
2008 27th Chinese Control Conference, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Li, Zhiqiang +3 more
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2013
The development of the preceding three chapters focused on complex systems of homogeneous polynomial equations. The main algorithmic results in these chapters were satisfying: we can compute an approximate zero of a system f in average (and even smoothed) randomized polynomial time. Central in these results were the consideration of complex numbers for
Peter Bürgisser, Felipe Cucker
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The development of the preceding three chapters focused on complex systems of homogeneous polynomial equations. The main algorithmic results in these chapters were satisfying: we can compute an approximate zero of a system f in average (and even smoothed) randomized polynomial time. Central in these results were the consideration of complex numbers for
Peter Bürgisser, Felipe Cucker
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Homogeneous Polynomial Systems
2013We finished the preceding chapter with a notion of approximate zero of a function and an algorithmic scheme to compute these approximate zeros, the adaptive homotopy.
Peter Bürgisser, Felipe Cucker
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Polynomial first integrals for quasi-homogeneous polynomial differential systems
Nonlinearity, 2002Here, several results concerning first integrals of homogeneous polynomial systems of differential equations are generalized to quasi-homogeneous polynomial systems. Properties of such systems are characterized in terms of the eigenvalues of the associated Kowalevskaya matrix.
Llibre, Jaume, Zhang, Xiang
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A Hybrid Polynomial System Solving Method for Mixed Trigonometric Polynomial Systems
SIAM Journal on Numerical Analysis, 2008Mixed trigonometric polynomial systems arise in many fields of science and engineering. Commonly, this class of systems is transformed into polynomial systems by variable substituting and adding some quadratic equations, and then solved by some polynomial system solving method.
Bo Yu, Bo Dong
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Stability of Polynomial Systems via Polynomial Lyapunov Functions
2007 Chinese Control Conference, 2006The stability of a class of polynomial systems is investigated by constructing a polynomial Lyapunov function. The key technique is to convert the polynomial Lyapunov candidate and it derivative into formal quadratic forms and to test their positivity and negativity respectively.
Qi Hongsheng, Cheng Daizhan
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1995
Numerical or analytical investigation of systems of differential equations is usually greatly facilitated if the right-hand sides of the equations are polynomials with respect to the unknown functions (polynomial systems). Such systems occur quite naturally in celestial mechanics in dealing with solutions in the vicinity of some known particular ...
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Numerical or analytical investigation of systems of differential equations is usually greatly facilitated if the right-hand sides of the equations are polynomials with respect to the unknown functions (polynomial systems). Such systems occur quite naturally in celestial mechanics in dealing with solutions in the vicinity of some known particular ...
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A Polynomial Membership Function Approach for Stability Analysis of Fuzzy Systems
IEEE Transactions on Fuzzy Systems, 2021Wen-Bo Xie, Hak-Keung Lam, Jian Zhang
exaly