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

[ \beginalign* \dot\mathbfx(t) &= \mathbff(\mathbfx(t), \mathbfu(t), t) \ \mathbfy(t) &= \mathbfh(\mathbfx(t), \mathbfu(t), t) \endalign* ]

[ \dotV \leq -\alpha V(\mathbfx) + \epsilon ] [ \beginalign* \dot\mathbfx(t) &= \mathbff(\mathbfx(t)

This means there exists a control law that can decrease (V) at every point. The famous provides a universal stabilizing controller when a CLF is known: t) \ \mathbfy(t) &= \mathbfh(\mathbfx(t)

[ \beginalign* \dotx_1 &= f_1(x_1) + g_1(x_1)x_2 \ \dotx_2 &= f_2(x_1,x_2) + g_2(x_1,x_2)u \endalign* ] x_2) + g_2(x_1

[ \mathbfu_\textrob = -\rho(\mathbfx) , \textsign\left( \frac\partial V\partial \mathbfx \mathbfg(\mathbfx) \right) ]