Stability of Planar Switched Systems: The Linear Single Input Case.

SIAM J. Control and Optimization 01/2002; 41:89-112. DOI: 10.1137/S0363012900382837
Source: DBLP

ABSTRACT 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 ∈ R,. In the space of these parameters, the shape and the convexity of the region in which there is stability are studied. This bidimensional problem assumes particular interest since linear systems of higher dimensions can be reduced to our situation. Key words. stability, planar, random switching function, switched systems AMS subject classifications. 93D20, 37N35 PII. S0363012900382837

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