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Solving standard continuous-time algebraic Riccati equations using the structure-exploiting Hamiltonian approach is briefly presented. A new solver based on the SLICOT Library subroutines has been developed and tested on the CAREX benchmark collection included in SLICOT. The numerical results show similar or better accuracy (in terms of the relative residuals, or relative errors, when exact solutions...
This paper investigates the existence and representation of stabilizing solutions to a class of generalized algebraic Riccati equation (GARE), which is often encountered in analysis and synthesis problems of continuous-time descriptor systems, such as H1 control and positive real control. The GARE under consideration consists of a couple of equations AT X + XT A + XT RX + Q = 0 and ET X = XTE ?? 0,...
Numerical algorithms for solving the continuous-time algebraic Riccati matrix equation on a distributed memory parallel computer are considered. In particular, it is shown that the Schur method, based on computing the stable invariant subspace of a Hamiltonian matrix, can be parallelized in an efficient and scalable way. Our implementation employs the state-of-the-art library ScaLAPACK as well as...
This note deals with linear-quadratic Stackelberg differential games including time preference rates with an open-loop information structure. The properties of the characteristic matrix associated with the necessary conditions for a Stackelberg strategy are pointed out. It is shown that such a matrix exhibits a special symmetry property of its eigenvalues. Sufficient conditions to guarantee a predefined...
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