期刊
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
卷 48, 期 5, 页码 885-890出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2003.811274
关键词
common quadratic Lyapunov function (QLF); stabilization; switched system
A topological structure, as a subset of [0, 2pi)(L) x R-+(n-1), is proposed for the set of quadratic Lyapunov functions (QLFs) of a given stable linear system. A necessary and sufficient condition for the existence of a common QLF of a finite set of stable matrices is obtained as the positivity of a certain integral. The structure and the conditions are considerably simplified for planar systems. It is also proved that a set of block upper triangular matrices share a common QLF, iff each set of diagonal blocks share a common QLF.
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