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- W3204353742 abstract "A linear dynamical system is called <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$k$</tex-math></inline-formula> -positive if its dynamics maps the set of vectors with up to <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$k-1$</tex-math></inline-formula> sign variations to itself. For <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$k=1$</tex-math></inline-formula> , this reduces to the important class of positive linear systems. Since stable positive linear time-invariant systems always admit a <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>diagonal</i> quadratic Lyapunov function, i.e., they are diagonally stable, we may expect that this holds also for stable <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$k$</tex-math></inline-formula> -positive systems. We show that, in general, this is not the case both in the continuous-time and discrete-time (DT) case. We then focus on DT <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$k$</tex-math></inline-formula> -positive linear systems and introduce the new notion of the <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>DT <inline-formula><tex-math notation=LaTeX>$k$</tex-math></inline-formula>-diagonal stability</i> . It is shown that this is a necessary condition for the standard DT diagonal stability. We demonstrate an application of this new notion to the analysis of a class of DT nonlinear systems." @default.
- W3204353742 created "2021-10-11" @default.
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- W3204353742 date "2022-08-01" @default.
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- W3204353742 title "Diagonal Stability of Discrete-Time $k$-Positive Linear Systems With Applications to Nonlinear Systems" @default.
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- W3204353742 doi "https://doi.org/10.1109/tac.2021.3115443" @default.
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