Title :
A new discrete impulse response Gramian and its application to model reduction
Author :
Azou, S. ; Brehonnet, P. ; Vilbé, P. ; Calvez, L.C.
Author_Institution :
Lab. d´´Electron. et Syst. de Telecommun., CNRS, Brest, France
fDate :
3/1/2000 12:00:00 AM
Abstract :
Some fundamental properties of an impulse response Gramian for linear, time-invariant, asymptotically stable, discrete single-input-single-output (SISO) systems are derived. This Gramian is system invariant and can be found by solving a Lyapunov equation. The connection with standard controllability, observability, and cross Gramians is proven. The significance of these results in model-order reduction is highlighted with an efficient procedure
Keywords :
Lyapunov methods; asymptotic stability; controllability; discrete time systems; linear systems; observability; reduced order systems; transient response; Lyapunov equation; SISO systems; cross Gramians; discrete impulse response Gramian; linear time-invariant asymptotically stable discrete single-input-single-output systems; model reduction; Continuous time systems; Controllability; Delay; Equations; Frequency; Observability; Polynomials; Read only memory; Reduced order systems; System identification;
Journal_Title :
Automatic Control, IEEE Transactions on
