Dynamic Algorithms for Solving Coupled Algebraic Riccati Equations Arising in Mixed H2/H∞ Control for Scalar Linear Systems

The problem of mixed H2/H∞ control can be formulated as a two-player nonzero-sum differential game as done by Limebeer et al. in the 1990s. For linear systems the problem is characterised by two coupled algebraic Riccati equations. Solutions for such algebraic Riccati equations are not straight-forward to obtain, particularly for infinite-horizon problems. In this paper two algorithms for obtaining solutions for the coupled algebraic Riccati equations associated with the mixed H2/H∞ control problem for scalar, linear systems is provided along with illustrative numerical examples