Control of rational systems using linear-fractional representations and linear matrix inequalities
A nonlinear, time-invariant system \(\dot x=F(x)x+G(x)u\), \(y=H(x)+J(x)u\), where the matrices are rational functions, is transformed to a `linear-fractional representation' \[ \dot x=Ax+B_uu+B_pp, \qquad q=C_qx+D_{qu}u+D_{qp}p, \qquad y=C_yx+D_{yu}u+D_{yp}p, \] \(p=\text{diag} (x_1I_{r1},\dots,x_nI_{rn})\), i.e. as a linear time-invariant system with a feedback connection between some fictious vector input \(p\) and fictious vector output \(q\). The feedback matrix is linear in the state vector \(x\) and its integers \(r_1,\dots,r_n\) reflect the `degree of nonlinearity'. Both state-feedback and dynamic output-feedback controller synthesis are adressed. As an example a controlled Van der Pol system is stabilized.
scientific article; zbMATH DE number 946988
scientific article