Stabilization of Linear Large-Scale Systems with Time Delays

Abstract

Large-scale systems with time delay are often seen in chemical processes and many other systems. In this paper we consider the problem of stabilizing linear large-scale systems with time delay (LSD) described by differential-difference equations
x_i(t)=A_ix_i(t)+∑^N_j=1F_ijx_j(t)+∑^N_j=1D_ijx_j(t-h_ij)+b_iu_i(t), i=1, 2, …, N,
where A_i, b_i are of the companion from, by using local feedback laws
u_i(t)=k_i^Tx_i(t), i=1, 2, …, N. Such a stabilization problem is studied for linear large-scale systems without time delay (LS) by many researchers, and some sufficient conditions for stablizability are derived in terms of the structure of interconnection matrices F_ij.
The objective of this paper is to extend these conditions for LS to LSD. The stabilizability condition obtained here is given as form of the interconnection matrices F_ij and D_ij to be satisfied, which can be calculated easily by using a computer, and coincide one for LS by setting D_ij=0. It should be noted that the conditions obtained here are applicable to LSD whose subsystems are with multi-input, by decomposing each subsystem the set of some single-input systems.