Implementation of state and output transformations

I am trying to convert a linear system with actuator and sensor faults and disturbances into two sub-systems with actuator and sensor faults respectively using state and output transformations, for fault detection. I am following the transformation technique used in the paper, "Simultaneous robust actuator and sensor fault estimation for uncertain non-linear Lipschitz systems" by Jian Zhang, Akshya Kumar Swain, Sing Kiong Nguang. Screenshots of the mathematical formulations are given below:

I am able to find out the appropriate T and S matrices and satisfy the given constraints. But I am a bit confused regarding the matrices A2 and A3. They won't be square matrices so how to implement them in MATLAB for simulation (I was thinking of using the state space block in Simulink but it requires a square system dynamics matrix)? Should I augment with zeros? Or are there any other techniques for suitable implementation of these transformations? Any help is appreciated.

Answer 1

[Divyajyoti Nayak]

Hi @Qandeel,

The 'State Space' block in Simulink is for linear state space systems. The system in the paper provided is non-linear and hence can't be represented by the block. The system needs to be modelled manually for simulation.

[Qandeel]

I am using the transformation technique only, my system will be linear.