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- W2949166745 abstract "This paper is concerned with the stability problem for the planar linear switched system $dot x(t)=u(t)A_1x(t)+(1-u(t))A_2x(t)$, where the real matrices $A_1,A_2in R^{2times 2}$ are Hurwitz and $u(cdot) [0,infty[to{0,1}$ is a measurable function. We give coordinate-invariant necessary and sufficient conditions on $A_1$ and $A_2$ under which the system is asymptotically stable for arbitrary switching functions $u(cdot)$. The new conditions unify those given in previous papers and are simpler to be verified since we are reduced to study 4 cases instead of 20. Most of the cases are analyzed in terms of the function $Gamma(A_1,A_2)={1/2}(tr(A_1) tr(A_2)- tr(A_1A_2))$." @default.
- W2949166745 created "2019-06-27" @default.
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- W2949166745 date "2008-09-22" @default.
- W2949166745 modified "2023-09-25" @default.
- W2949166745 title "A note on stability conditions for planar switched systems" @default.
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