Hello all, good day.

I am a PhD student doing a course project in optimal control and stumbled upon an issue while trying to implement a load current observer for the UPS inverter system (attached with this post).

The issue I am facing is with the matrices describing the observer dynamics presented in the paper in section IV. The matrices Ao and Bo are having the first two rows set to zeros, which would make the system uncontrollable. Therefore the first two states are unaffected no matter what the control is. This is (understandably) hindering with the solution to the Algebraic Riccati Equation solution Equation 17 in the paper attached (which I am attempting to solve via care.m in Matlab; Matlab throws an error whenever I compute it).

Is this a mistake in the paper or a mistake in my understanding? Any insights will be appreciated.

Thank you.