In terms of a piecewise affine system representation, which is a kind of hybrid system model, this article discusses a series of approaches to modelling, analysing and synthesizing a biological network such as a gene-regulatory network. First, the input assignment problem, the controllable state set problem (CSP) and the input trajectory generation problem are emphasized as control problems to be addressed for biological networks. Subsequently, after the modelling issue on biological networks developed in the systems and control community is briefly explained, the CSP is described in detail with reference to control of the quorum-sensing system in the pathogen Pseudomonas aeruginosa. Finally, an optimal control design method to the quorum-sensing system is proposed as a solution to the input trajectory generation problem.