Robust Nonlinear Control Design State Space And Lyapunov Techniques Systems Control Foundations Applications

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Choose (V = \frac12\mathbfx^T\mathbfP\mathbfx + \frac12\tilde\theta^T\Gamma^-1\tilde\theta), where (\tilde\theta = \hat\theta - \theta). The update law (\dot\hat\theta = -\Gamma \mathbfY(\mathbfx)^T \frac\partial V\partial \mathbfx) ensures (\dotV \leq 0). This is a powerful robust nonlinear method because it combines robustness (disturbances) with adaptation (parametric uncertainty).