An algorithm for solving the singularly perturbed \(H_\infty\) algebraic Riccati equation (Q1806600)

An iterative procedure to compute the stabilizing solution to an algebraic Riccati equation associated to a singularly perturbed linear system is presented. The algebraic Riccati equation of singularly perturbed \(H_\infty\) linear-quadratic optimal control problems is decoupled into two completely independent, reduced-order, pure-slow and pure-fast \(H_\infty\) algebraic Riccati equations. Even though the algebraic Riccati equations obtained are nonsymmetric, they are efficiently solved in terms of Lyapunov iterations by using the Newton method. The presented algorithm can be used for \(H_\infty\) parallel filtering and regulation of systems displaying two-time scale dynamics.