Extended Matrix Pencils for the Delta-Operator Riccati Equation

Modern optimal control techniques such as H2 and H1 control rely on the solution of algebraic Riccati equations for controller synthesis. Reliable numerical techniques for numerical computation of the solution of these equations have been proposed using eigenvector or Schur decompositions of Hamiltonian matrices for continuous-time algebraic Riccati equations (CARE), or symplectic matrices for discrete-time (Z-transform) algebraic Riccati equations (DARE) [12, 6]. An improved solution method for the DARE was proposed in [9] in terms of a generalized eigenvalue problem which is equivalent to the symplectic decomposition and which does not require that the state dynamics matrix be invertible. This approach provides a computationally efcient algorithm for singular and ill-conditioned problems.