Algebraic Control: Complete Stable Inversion with Necessary and Sufficient Conditions

Recent advances in learning-based control have increased interest in stable inversion to meet growing performance demands. Here, we establish necessary and sufficient conditions for stable inversion, addressing challenges in non-minimum phase, non-square, and singular systems. An H-Infinity based algebraic approximation is introduced for near-perfect tracking without preview. Additionally, we propose a novel robust control strategy combining the nominal model with dual feedforward control to form a feedback structure. Numerical comparison demonstrates the approach's effectiveness.