TAG ARCHIVE

asymptotic-stability

1 MARIA OS blog articles tagged asymptotic-stability, organized as a Bonginkan topic archive for search engines and LLM retrieval.

1 article|Published by Bonginkan

Responsibility Gates and AI Governance

Safety, accountability, fail-closed gates, auditability, and human-in-the-loop control for AI agents.

Multi-Agent Mathematics

Formal models for convergence, stability, game theory, graph dynamics, and multi-agent evaluation.

Evidence, RAG, and Knowledge Governance

Evidence bundles, retrieval architecture, Graph RAG, knowledge trust, and auditable reasoning pipelines.

MathematicsJanuary 12, 202628 min read

Fail-Closed Design Enhances Stability: A Lyapunov Analysis of Governance Dynamics

Proving that fail-closed gates create a stable equilibrium in the risk-velocity state space using Lyapunov's direct method

Enterprise AI governance systems can accumulate risk over time through compounding errors, configuration drift, and expanding autonomy. This paper models governance dynamics as a continuous-time state system with risk `r` and decision velocity `v`, and control inputs gate strength `g` and evidence quality `q`. Using Lyapunov candidate `V(r, v) = alpha*r^2 + beta*v^2`, we derive conditions on `g` and `q` such that `dV/dt < 0`, establishing asymptotic stability. The resulting stability region in `(g, q)` space provides a design specification for bounded risk accumulation.

lyapunov-stabilityfail-closedcontrol-theoryrisk-dynamicsgovernance-designasymptotic-stability