Abstract
Hadamard synergic control is a new kind of control problem which is achieved via a composite strategy of the state feedback control and the direct regulation of the part of connection coefficients of system state variables. Such a control is actually used very often in the practical areas. In this paper, we discuss Hadamard synergic stabilization problem for a class of dynamical networks. We analyze three cases: 1) Synergic stabilization problem for the general twonodenetwork. 2) Synergic stabilization problem for a special kind of networks. 3) Synergic stabilization problem for special kind of networks with communication timedelays. The mechanism of the synergic action between two control strategies: feedback control and the connection coefficients regulations are presented.
Highlights
Complex networks of dynamic agents have attracted great interesting in recently years
Hadamard synergic control is a new kind of control problem which is achieved via a composite strategy of the state feedback control and the direct regulation of the part of connection coefficients of system state variables
We present the formulations of the Hadamard synergic stabilization problems as follows: Hadamard synergic stabilization problem (HSSP) [21]: Given system (1), and let A A1 A2
Summary
Complex networks of dynamic agents have attracted great interesting in recently years. A new kind of concept called Hadamard synergic control is introduced based on the Hadamard matrix product [16] It is achieved via a composite strategy of the state feedback control and the direct regulation of the part of connection coefficients of system state variables. Such a control improves the limitations of the traditional feedback control [17,18,19] and may be of some potential applications in the emergency treatment such as isolation and obstruction control. Consider the network model researched in [1,3], the system interconnection matrix A is divided into two parts. From the definition of the matrix Kronecker product we know, the connection matrix of the system has very symmetrically consistency structure if we describe the system by using the corresponding Hadamard product, this is: any two subsystems have the same basic connection structure except the coupling coefficient, i.e
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