Title :
2-D Lyapunov equation and filter design based on the Fornasini-Marchesini second model
Author_Institution :
Fac. of Eng., Hiroshima Univ., Japan
fDate :
2/1/1993 12:00:00 AM
Abstract :
A two-dimensional (2-D) Lyapunov equation with constant coefficients is considered for the Fornasini-Marchesini second local state-space (LSS) model. First, a novel criterion relating to the Lyapunov equation is presented that sufficiently guarantees the asymptotic stability. A sufficiency condition that ensures the absence of limit cycles is also given. Next, the above stability condition is incorporated into the 2-D filter structure to design 2-D state-space digital filters with guaranteed asymptotic stability. An efficient method is then developed for computing the characteristic polynomial and the inverse of the system matrix. Finally, two numerical examples are given to design 2-D stable state-space digital filters
Keywords :
Lyapunov methods; filtering and prediction theory; limit cycles; stability; stability criteria; state-space methods; two-dimensional digital filters; 2D equation; 2D state-space digital filters; Fornasini-Marchesini second model; Lyapunov equation; asymptotic stability; characteristic polynomial; constant; filter design; limit cycles; stability condition; state-space model; system matrix inverse; Asymptotic stability; Delay; Differential equations; Digital filters; Finite wordlength effects; Limit-cycles; Polynomials; Senior members; Two dimensional displays;
Journal_Title :
Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on