Stabilization of Periodic Switched k-Valued Logical Networks

Abstract

The stabilization of periodic switched k-valued logical networks is investigated in this paper, and some new results are presented. The system considered consists of several k valued logical networks and these networks run in a periodic switching law. First, by using the Cheng product of matrices, a periodic switched k-valued logical (control) network is transformed into a discrete dynamic system which is written as an algebraic form. Second, the switching-state space and the switching-input-state space are defined. Then combining with the algebraic form, some necessary and sufficient conditions for the stability and the stabilization are obtained. An algorithm to find the input sequence that stabilizes the system is also provided. Finally, illustrative examples are given to support the proposed new results.

Survey on Mathematical Models and Methods of Complex Logical Dynamical Systems

“…Stability of switched k-valued logical networks was investigated in [96,97]. Stabilization and control design of switched k-valued logical networks were investigated in [6,98,99]. Controllability of switched mix-valued logical networks with constraints was investigated in [100].…”

“…where x i , i = 1, • • •, m are state variables, v j , j = 1, • • •, n are control inputs, y p , p = 1, • • •, q are outputs, ϕ i , i = 1, • • •, m are logical functions determining the state evolution of system (1), and ψ p , p = 1, • • •, q are logical functions determining the output evolution of system (1). Furthermore, (1) is called k-valued logical networks [6,7]; 1) is called mix-valued logical networks [8][9][10].…”