Novel Contributions This work introduces the Recursive Feedback Loop Framework (RFLF), a general mathematical formalism that extends classical feedback and control models by explicitly incorporating deep recursion, memory kernels, and information-theoretic flow. Unlike standard state-space or Markovian formulations, RFLF allows system evolution to depend on arbitrarily deep historical composition through recursive operators. The framework unifies discrete and continuous dynamics, linear and nonlinear feedback, deterministic and stochastic evolution, and delayed memory effects within a single operator-based structure. Key contributions include: A recursive operator formulation capturing multi-depth temporal feedback. A unified differential–integral feedback equation with memory kernels. Stability and convergence guarantees under bounded-gain and energy constraints. Integration of information-theoretic measures (Kullback–Leibler divergence) to quantify causal feedback flow. Compatibility with classical control theory (transfer functions, PID control) while extending beyond it. The framework is domain-agnostic and applicable to control systems, adaptive computation, learning dynamics, and complex systems with memory.
Jose Roberto Jimenez (Thu,) studied this question.