Stability Conditions for Adaptive Control of Uncertain Dynamical Systems with Actuator and Unmodeled Dynamics

In many practical applications, the effects of both actuator and unmodeled dynamics are strongly present in feedback loops. In this paper, we consider adaptive control of uncertain dynamical systems subject to both actuator and unmodeled dynamics. Specifically, utilizing Lyapunov stability theory, linear matrix inequalities, and matrix mathematics, we reveal two sufficient stability conditions. The first one captures the system-theoretic tradeoff between system uncertainties and actuator dynamics, and the second one depends on the first one as well as the matrices resulting from the unmodeled dynamics. An illustrative numerical example is also provided to demonstrate our findings involving these stability conditions.