Controllability and Observability of Boolean Control Networks With Time-Variant Delays in States

: Lijun Zhang, Kuize Zhang

Publisher: IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC

: PISCATAWAY; 445 HOES LANE, PISCATAWAY, NJ 08855-4141 USA

: 2013

IEEE Transactions on Neural Networks and Learning Systems

: Ieee Transactions on Neural Networks and Learning Systems

: IEEE Trans.Neural Netw.Learn.Syst.

: 9

: 24

: 9

: 1478

: 1484

: 8

: 2162-237X

DOI: https://doi.org/10.1109/TNNLS.2013.2246187

This brief investigates the controllability and observability of Boolean control networks with (not necessarily bounded) time-variant delays in states. After a brief introduction to converting a Boolean control network to an equivalent discrete-time bilinear dynamical system via the semi-tensor product of matrices, the system is split into a finite number of subsystems (constructed forest) with no time delays by using the idea of splitting time that is proposed in this brief. Then, the controllability and observability of the system are investigated by verifying any so-called controllability constructed path and any so-called observability constructed paths in the above forest, respectively, which generalize some recent relevant results. Matrix test criteria for the controllability and observability are given. The corresponding control design algorithms based on the controllability theorems are given. We also show that the computing complexity of our algorithm is much less than that of the existing algorithms.