TY - JOUR

T1 - Stabilization of discrete systems by dynamic regulator

AU - Zuber, I.E.

PY - 2012

Y1 - 2012

N2 - We consider the system x k+1=A kx k+b ku k,u= k+1=m k *x k,k=1,2,..., where A k ∈ ℝ n×n, b k ∈ ℝ n, and m k ∈ ℝ n. We assume that A k is a Frobenius matrix, the last component of vector b k is zero, and all entries of A k and b k are bounded for all k. Lyapunov quadratic function with diagonal matrix of coefficients is used to find coefficients m k and restrictions on coefficients b k which make the system globally asymptotically stable.

AB - We consider the system x k+1=A kx k+b ku k,u= k+1=m k *x k,k=1,2,..., where A k ∈ ℝ n×n, b k ∈ ℝ n, and m k ∈ ℝ n. We assume that A k is a Frobenius matrix, the last component of vector b k is zero, and all entries of A k and b k are bounded for all k. Lyapunov quadratic function with diagonal matrix of coefficients is used to find coefficients m k and restrictions on coefficients b k which make the system globally asymptotically stable.

UR - https://elibrary.ru/item.asp?id=20494146

M3 - Article

VL - 45

SP - 22

EP - 25

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 1

ER -