Title :
Sensitivity of the stable discrete-time Lyapunov equation
Author :
Gahinet, Pascal M. ; Laub, Alan J. ; Kenney, Charles S. ; Hewer, Gary A.
Author_Institution :
Nat. Inst. for Res. in Comput. & Control Sci., Rocquencort, France
fDate :
11/1/1990 12:00:00 AM
Abstract :
The sensitivity of the stable discrete-time Lyapunov equation is analyzed through the spectral norm of the inverse Lyapunov operator. This leads to a directly computable easy-to-interpret sensitivity measure, which involves only the open-loop state matrix and also provides insight into the connection between sensitivity, stability radius, and conditioning of the eigenproblem of the open-loop state matrix. These results are an extension, to the discrete-time case, of analogous results for the continuous-time Lyapunov equation
Keywords :
Lyapunov methods; discrete time systems; eigenvalues and eigenfunctions; matrix algebra; sensitivity analysis; stability; eigenproblem; open-loop state matrix; sensitivity; spectral norm; stability; stable discrete-time Lyapunov equation; Closed-form solution; Contracts; Equations; Lakes; Military computing; Performance analysis; Spectral analysis; Stability; Vectors; Weapons;
Journal_Title :
Automatic Control, IEEE Transactions on
