Robust Dynamic Output Feedback Controller Design Using Linear Matrix Inequalities (LMIs)

Robust control serves as a critical methodology for addressing system uncertainties and external disturbances. The design of dynamic output feedback controllers through Linear Matrix Inequalities (LMIs) effectively resolves challenges in system stability and performance optimization.

During the design process, the first step involves establishing the system's state-space model while accounting for parameter uncertainties or external disturbances. Through Lyapunov stability theory, the controller's existence conditions are transformed into a set of LMI constraints. These constraints guarantee closed-loop system stability under uncertain conditions while enhancing performance metrics through objective function optimization. In code implementation, this typically involves constructing matrices A, B, C, D representing the system dynamics and defining uncertainty bounds using norm-bounded or polytopic approaches.

Dynamic output feedback controllers utilize measurable system output signals combined with dynamic compensation mechanisms, significantly improving control flexibility. Compared to static feedback, they demonstrate superior adaptability to complex operating conditions. The integration of LMI toolboxes (such as MATLAB's LMI Toolbox or YALMIP) streamlines the controller synthesis process, enabling efficient solutions while supporting multi-objective optimization with various performance constraints. Key functions like feasp or mincx in MATLAB help solve the feasibility and optimization problems respectively.

In practical applications, this methodology demonstrates exceptional performance in domains requiring high robustness, such as robotic control and aircraft navigation. By adjusting weight matrices in the LMI formulation, designers can achieve optimal balance between system response speed and disturbance rejection capabilities. The implementation typically involves iterative tuning of Q and R matrices in the quadratic performance index to meet specific design requirements.