Quadratic optimal controller to stabilise symmetrical systems

In this paper, we design a controller for stabilising a control system. The technique used for designing the controller includes a linear regulator and an asymptotical observer which form the controller. The linear regulator designed is a feedback of estimated states and also it must minimise a quadratic performance index. The gain matrix of optimal feedback is obtained by solving the Riccati equation, whilst the gain observer matrix is computed by making use of symmetrical systems properties. The properties of symmetrical systems allow us to find the optimal gain matrix of the observer without solving the dual Riccati equation, we only need to compute the matrices of controllability and observability. Having calculated the gain matrices of regulator and of observer, we proceeded to compute the transfer function of the observer-based controller.