Optimal Dynamic Output Feedback Design for Continuous-Time Linear Time-Invariant Systems

This letter presents iterative methods to design optimal controller-observer pairs for dynamic output feedback control of continuous-time linear time-invariant systems. We propose a novel design formulation based on the linear optimal control framework with additional structural constraints. Using Lyapunov stability theory and algebraic manipulations, we reformulate the complex optimization problem into a computationally viable format. We present a gradient-descent-based algorithm to solve this optimization problem effectively. Finally, we validate our proposed theories through numerical examples.