M-Matrix-Based State Observer Design for Genetic Regulatory Networks With Mixed Delays

Understanding genetic regulatory networks (GRNs) and designing a controller requires access to all the states of the system. However, not all the states of GRN can be experimentally measured in practice. Therefore, a state observer is necessary to estimate the unknown states from measured data. In this brief, we use M-matrix theory to design stable state observers for GRNs with mixed delays. Different from the linear matrix inequalities-based method, we formulate the state observer design as a feasible set problem which can be easily solved by some programming solvers with the optimization principle. The simulation results illustrate the effectiveness of our design approach.