# zbMATH — the first resource for mathematics

A new approach for global controllability of higher order Boolean control network. (English) Zbl 1327.93073
Summary: Using the semi-tensor product, the global control problem of the higher order Boolean control network with avoiding set is considered. First, the number of different control sequences that drive the higher order Boolean control network from the initial state to the destination state while avoiding undesirable set is provided. Then, the definition of global controllability of higher order Boolean control network is given. Third, by using the classical theory of nonnegative matrices, a necessary and sufficient condition for the global controllability of higher order Boolean control network with avoiding set is presented. Furthermore, a sufficient condition for $$k$$ fixed-time global controllability of the system is also obtained. At last, an example is given to illustrate the main results.

##### MSC:
 93B05 Controllability 94C05 Analytic circuit theory 93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
Full Text: