Further results on expansion design of partially decentralized controllers: 2x2 plant cases

An expansion procedure to design partially decentralized controllers was re cently proposed. This method requires the operation of pseudo-inverse of no n-square matrices, which is not unique. Thus, it introduces an extra design freedom, which was not addressed in the previous studies. In this paper, t he effect of the pseudo-inverse on the stability and performance of 2 x 2 p artially decentralized control systems is studied. Specifically, the range of the pseudo-inverse factors arising from the stability condition of the c ontrol system is derived. In addition, an 'ideal' pseudo-inverse factor, wh ich minimizes interaction in the control system, is obtained based on the c oncept of non-square block relative gain. Simulation results show that a pa rtially decentralized controller with the 'ideal' pseudoinverse factor give s an improved controller performance.