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Robust stabilization in a single-link biomechanical model: a time-domain analysis

In this paper we analyze the robust stabilization of posture in a single-link biomechanical model with force feedback, dual position and velocity feedback, and with delays in all the three feedback loops. The model is physiologically motivated and represents gross approximation of the human neuromusculoskeletal system in the sagittal plane. The feedback paths in the model represent proprioceptive feedback from muscle spindle (MS) and the Golgi tendon organ (GTO), and include the latencies present in the physiological system. Lyapunov functional approach is used to guarantee asymptotic stability with arbitrary feedback delays. The approach leads to linear matrix inequality (LMI)-based delay-independent conditions requiring solution of a set of finite-dimensional algebraic Riccati inequalities. The framework can be extended to Hinfin feedback control synthesis for single and multi-link robotic models with state or feedback delays