Title :
Identification/reduction to a balanced realization via the extended impulse response Gramian
Author :
Ang, E.-J. ; Sreeram, V. ; Liu, W.Q.
Author_Institution :
Dept. of Electr. & Electron. Eng., Western Australia Univ., Nedlands, WA, Australia
Abstract :
A new state space model reduction algorithm for linear, discrete time-invariant (LDTI) systems is proposed which is based on the extended impulse response Gramian first defined here for LDTI systems. The reduction algorithm employs singular value decomposition to retain states corresponding to dominant singular values of these Gramians. The proven properties of the reduced order models include convergence to a balanced realization with conditional controllability, observability and asymptotic stability. A suboptimal property of the model is also demonstrated. Finally, an error bound is obtained for this algorithm. In addition to model reduction, the proposed technique can also be applied to system identification from impulse response data of deterministic or stochastic nature
Keywords :
asymptotic stability; controllability; convergence; discrete systems; identification; linear systems; observability; realisation theory; reduced order systems; singular value decomposition; state-space methods; transient response; asymptotic stability; balanced realization; conditional controllability; dominant singular values; error bound; extended impulse response Gramian; identification/reduction; linear discrete time-invariant systems; observability; reduced order models; singular value decomposition; state space model reduction algorithm; Asymptotic stability; Controllability; Convergence; MIMO; Observability; Reduced order systems; Singular value decomposition; State-space methods; Stochastic systems; System identification;
Conference_Titel :
Decision and Control, 1995., Proceedings of the 34th IEEE Conference on
Conference_Location :
New Orleans, LA
Print_ISBN :
0-7803-2685-7
DOI :
10.1109/CDC.1995.478617
