A control lyapunov function approach to feedback stabilization of logical control networks

Abstract

This paper studies the feedback stabilization problem of k-valued logical control networks (KVLCNs), and proposes a control Lyapunov function (CLF) approach for this problem. First, the CLF is defined for KVLCNs, and it is proved that the existence of state feedback stabilizers is equivalent to the existence of CLF. Second, two necessary and sufficient conditions are presented for the existence of CLF, based on which, all possible state feedback stabilizers are characterized by finding all admissible sets of control Lyapunov inequalities. Third, the concept of convergence index vector is defined for KVLCNs, and it is shown that for a given admissible set of control Lyapunov inequalities, the CLF is unique in the sense of convergence index vector. Finally, the obtained new results are applied to regulation of the lactose operon in Escherichia coli, stabilization of switched KVLCNs, and strategy consensus of networked evolutionary games, respectively.