Title :
Minimization of L2-Sensitivity for Linear Discrete-Time Systems Subject to L2-Scaling Constraints Using a Lagrange Function and a Bisection Method
Author :
Hinamoto, Takao ; Oumi, Toru
Author_Institution :
Graduate Sch. of Eng., Hiroshima Univ.
Abstract :
In this paper, the problem of minimizing an L2-sensitivity measure subject to L2-norm dynamic-range scaling constraints for linear discrete-time systems is investigated. To this end, an expression for evaluating the L2-sensitivity is introduced and an L2-sensitivity minimization problem subject to the L2-scaling constraints is formulated. An efficient iterative algorithm is then explored to solve the constraint optimization problem directly. The proposed solution method relies on neither converting the constrained optimization problem into an unconstrained one nor using a quasi-Newton algorithm, but utilizes a Lagrange function, some matrix-theoretic techniques, and a bisection method. The optimal state-space model structure with minimum L 2-sensitivity and no overflow oscillations is constructed by applying an appropriate coordinate-transformation matrix. A numerical example is presented to illustrate the utility of the proposed technique
Keywords :
discrete time systems; iterative methods; linear systems; matrix algebra; minimisation; L2-sensitivity minimization; Lagrange function; bisection method; constraint optimization problem; coordinate-transformation matrix-theoretic techniques; dynamic-range scaling constraints; iterative algorithm; linear discrete-time systems; optimal state-space model structure; Computer simulation; Constraint optimization; Finite wordlength effects; Iterative algorithms; Lagrangian functions; Linear systems; Matrix converters; Minimization methods; Quantization; Transfer functions; L2-scaling constraints; L2-sensitivity minimization; Lagrange function; bisection method; linear discrete-time systems; no overflow oscillations;
Conference_Titel :
SICE-ICASE, 2006. International Joint Conference
Conference_Location :
Busan
Print_ISBN :
89-950038-4-7
Electronic_ISBN :
89-950038-5-5
DOI :
10.1109/SICE.2006.315353