BMI approach to cooperative control of linear systems with uncertainty and time-delay

The problem of designing cooperative controller of linear systems with uncertainty and time-delay is studied. Based on Lyapunov functional method, sufficient condition is given for cooperative stabilization of combined system composed by two systems. And then the problem of designing cooperative controller is formulated into the non-convex optimization problem with bilinear matrix inequality (BMI) constraints by using BMI. And an alternate algorithm is provided for the optimal design of the controller. Finally, an illustrative example is provided to show the feasibility of our proposed method.