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

This is the essence of , one of the most powerful robust nonlinear methods.

Systems where time explicitly appears in the state equation ( This is the essence of , one of

Within the "Systems & Control: Foundations & Applications" framework, several specific strategies stand out: 1. Sliding Mode Control (SMC) Defining (\delta\mathbfx = \mathbfx - \mathbfx_0)

For a system (\dot\mathbfx = \mathbff(\mathbfx)) with (\mathbff(0)=0), if we can find a continuously differentiable function (V(\mathbfx)) such that: (\delta\mathbfu = \mathbfu - \mathbfu_0)

ẋ(t)=f(x(t),t)+g(x(t),t)u(t)+d(t)x dot open paren t close paren equals f of open paren x open paren t close paren comma t close paren plus g of open paren x open paren t close paren comma t close paren u open paren t close paren plus d open paren t close paren

A common first step is local linearization around an equilibrium point ((\mathbfx_0, \mathbfu_0)) where (\mathbff(\mathbfx_0, \mathbfu_0)=0). Defining (\delta\mathbfx = \mathbfx - \mathbfx_0), (\delta\mathbfu = \mathbfu - \mathbfu_0), we compute the Jacobian matrices: