6533b859fe1ef96bd12b75b5

RESEARCH PRODUCT

Stability of switched systems: The single input case

Ugo Boscain

subject

Pure mathematicsMeasurable functionExponential stabilityStability theoryMathematical analysisFunction (mathematics)Invariant (mathematics)Dynamical systemEigenvalues and eigenvectorsMathematicsLinear stability

description

We study the stability of the origin for the dynamical system x(t) = u(t)Ax(t) + (1 − u(t))Bx(t), where A and B are two 2×2 real matrices with eigenvalues having strictly negative real part, x ∊ R2 and u(.) : [0, ∞[→ [0,1] is a completely random measurable function. More precisely, we find a (coordinates invariant) necessary and sufficient condition on A and B for the origin to be asymptotically stable for each function u(.). This bidimensional problem assumes particular interest since linear systems of higher dimensions can be reduced to our situation.

yearjournalcountryeditionlanguage
2001-09-012001 European Control Conference (ECC)
https://doi.org/10.23919/ecc.2001.7076170