In modern distributed cloud environments, efficient resource allocation is required as traditional scaling mechanisms are often subject to cloud thrashing due to network-induced latencies. In this paper, we propose C-SAS (Complex-Stability Aware Scaling), an intelligent autonomous orchestration framework that leverages complex analytic methods to achieve system-wide equilibrium. In contrast to heuristic-based models, C-SAS acts as a stability-aware agent, converting telemetry noise into a deterministic "Safety Envelope" on the $s$-plane using the Argument Principle and Rouché's Theorem. The algorithm smartly suppresses oscillatory scaling operations that would otherwise degrade performance, by computing a real-time Analytic Stability Index (ASI). The experimental results show that C-SAS reduces VM flapping by 94\%, and achieves 96\% resource efficiency, significantly outperforming standard PID and ML-based autonomous agents. Our results suggest that future resilient autonomous cloud infrastructures will require AI-driven orchestrators with built-in formal stability constraints.