Joint Design of Disturbance Observer-Based Feedback Controllers for Discrete-Time Systems Subject to Actuator Faults

This paper proposes a novel iterative linear matrix inequality (LMI) method for a class of input-affine nonlinear systems. The design method incorporates nonlinearities through convex enclosure techniques, thereby ensuring the stability of the nonlinear control system. Furthermore, the controller gain is optimized through the application of LQ criteria, while the observer gains are optimized in order to suppress process and sensor noise. The LMI problem is solved by a block-diagonal structure of a common Lyapunov matrix to separate the controller from the observer in the design. The observer is composed of a disturbance observer and a state observer. Thus, the overall control structure suppresses the process and sensor noise and compensate disturbances such as actuator inaccuracies efficiently. An example demonstrates the effectiveness of the method by comparing it to linear-quadratic-Gaussian (LQG) controllers based on the linearized model. Therefore, the cosed loop simulation is based on the continuous-time nonlinear plant and the discrete-time linear observer-based state-feedback control structure.