Compliant manipulators equipped with Variable Stiffness Actuation (VSA) possess the ability to safely interact with their environment and adapt to complex tasks. However, the tracking performance of such manipulators is significantly influenced by their intrinsic compliance and varying stiffness. This paper presents a robust control strategy for compliant manipulators equipped with Discrete Variable Stiffness Actuation (DVSA), aimed at enhancing tracking performance under both fixed and varying stiffness conditions. By compensating for nonlinear dynamics, joint coupling, frictions, stiffness variability and uncertainties through a Sliding Perturbation Observer (SPO), the proposed approach ensures robust and consistent performance, significantly outperforming traditional controllers. In fixed stiffness scenarios, the proposed controller achieves a reduction in energy consumption of up to 68.1% at the lowest stiffness and 75.5% at the highest stiffness, demonstrating superior efficiency. For abrupt stiffness transitions (lowest-highest-lowest), the proposed controller reduces energy consumption by up to 70.9% compared to traditional controllers. Additionally, it maintains smooth control input and precise tracking, avoiding the chattering and inefficiencies that traditional controllers typically exhibit. The SPO effectively estimates all system states and perturbation, compensating for nonlinearities, disturbances due to variable stiffness, and friction, enabling consistent trajectory tracking with minimal control effort. The proposed controller's ability to adapt to varying stiffness levels without explicit parameter tuning highlights its robustness and practical viability. Simulation and experimental results validate its superior performance in reducing tracking error and energy consumption, particularly in scenarios where traditional controllers struggle to manage varying stiffness effectively.