Systematic linear matrix inequality conditions to design a robust decentralised observer-based optimal control for interconnected systems

This study discusses the optimal and robust decentralised observation and control scheme for interconnected systems composed of linear models with non-linear cross-coupling terms and uncertain parameters. The proposed control approach is formulated in a systematic optimisation problem subject to linear matrix inequality constraints to compute simultaneously the robust observer and control gain matrices. Indeed, it is developed to ensure the stability of the closed-loop system within the Lyapunov method, to minimise the upper bound of a cost function leading to optimal performances and to maximise the bound of non-linearity keeping the augmented system stable despite the uncertainties and non-linearities applied to the subsystems. A numerical simulation is carried out on a power system with three interconnected machines to illustrate the effectiveness and the high performances of the proposed control approach.