Title :
A common Lyapunov function for stable LTI systems with commuting A-matrices
Author :
Narendra, Kumpati S. ; Balakrishnan, Jeyendran
Author_Institution :
Dept. of Electr. Eng., Yale Univ., New Haven, CT, USA
fDate :
12/1/1994 12:00:00 AM
Abstract :
The paper demonstrates that a common quadratic Lyapunov function exists for all linear systems of the form x˙=Aix, i=1,2,···,N, where the matrices Ai are asymptotically stable and commute pairwise. This in turn assures the exponential stability of a switching system x˙(t)=A(t)x(t) where A(t) switches between the above constant matrices Ai
Keywords :
Lyapunov matrix equations; asymptotic stability; asymptotically stable matrices; common quadratic Lyapunov function; commuting A-matrices; exponential stability; linear systems; stable LTI systems; switching system; Adaptive control; Artificial intelligence; Control systems; Control theory; Intelligent control; Lyapunov method; Stability; Switches; Switching systems; Symmetric matrices;
Journal_Title :
Automatic Control, IEEE Transactions on
