Observer-embedded \(L_2\)-gain control (Q5938960)

The authors present a formulation with mixed linear matrix inequalities, a Hamiltonian matrix, and a linear parametrization to provide solutions to the feasible observer-embedded \(L_2\)-gain controllers for the following generalized plant: NEWLINE\[NEWLINE\left\{\begin{aligned}\dot x &= Ax + B_1w + B_2u,\\ z& = C_1x + D_{11}w + D_{12}u,\\ y& = C_2x + D_{21}w + D_{22}u, \end{aligned}\right.NEWLINE\]NEWLINE where the controller processes the measurable output signal \(y\) to generate the control signal \(u\) in presence of exogenous disturbances and modeling uncertainty \(w\). The paper demonstrates that the \(H_\infty\) controller of \textit{J.~C.~Doyle, K.~Glover, P.~P. Phargonekar} and \textit{B.~A.~Francis} [IEEE Trans. Autom. Control 34, 831-847 (1989)] can be reinterpreted as an observer-embedded \(L_2\)-gain controller. The embedded observer is similar to the conventional Luenberger observer except having an additional state-dependent calibration term that compensates for exogenous inputs and model uncertainties.