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- W2064883983 abstract "A class of nonlinear systems is considered in IR <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>2</sup> whose system's function is, component-wise, given by the product of real powers of the state's entries. We call it the class of 'Π-algebraic' systems. It is shown that every Π-algebraic nonlinear system undergoes a quadratic embedding into a suitable (non associative) algebra. This means that a product can be defined in the state-space, which makes the latter a non associative algebra, whose associated quadratic differential equation has a subset of entries of its solution equal to the solution of the original nonlinear system. We also study a related control problem, where for a meaningful subclass of the considered systems it is shown that a state-feedback regulator can be build up, having exponential performance, which makes the y-axe in IR <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>2</sup> a globally asymptotically stable equilibrium set of the closed-loop system." @default.
- W2064883983 created "2016-06-24" @default.
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- W2064883983 date "2013-05-01" @default.
- W2064883983 modified "2023-09-25" @default.
- W2064883983 title "Quadratic embedding into algebras and global stabilization for a class of nonlinear control systems" @default.
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- W2064883983 doi "https://doi.org/10.1109/carpathiancc.2013.6560505" @default.
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