We start with a discussion of coupled algebraic Riccati equations arising in the study of linear-quadratic optimal control problem for Markov jump linear systems. Under suitable assumptions, this system of equations has a unique positive semidefinite solution, which is the solution of practical interest. The coupled equations can be rewritten as a single linearly perturbed matrix Riccati equati...

In this paper, based on the fractional Riccati equation, we propose an extended fractional Riccati sub-equation method for solving fractional partial differential equations. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. By a proposed variable transformation, certain fractional partial differential equations are turned into fractional ordinary di...

The numerical solution of matrix algebraic Riccati equations with condition and forward error estimates is considered. A comparison of the accuracy of Schur and matrix sign function methods in the solution of high order Riccati equations is done.

The H 2 optimization problem with preview and asymptotic behavior constraints is considered in a general two-sided model matching setting. The solution is obtained in terms of two constrained Sylvester equations, associated with asymptotic behavior, and stabilizing solutions of two algebraic Riccati equations. The Riccati equations do not depend on the preview length, yet are affected by asympt...

Both linear time-invariant (LTI) and linear time-varying (LTV) systems are addressed. They are placed in a unified conceptual framework. The characteristic equation for each subclass is formulated as a Riccati equation. Where LTI-systems lead to algebraic Riccati equations, the LTV-case generalizes this result to differential Riccati equations.

In this note we show that the flow of matrix Riccati equations is monotone. Consequently, many results for Riccati equations can be obtained easily using standard as well as more recent results from the theory of monotone systems.

We consider the nonsymmetric algebraic Riccati equation for which the four coefficient matrices form an M -matrix. Nonsymmetric algebraic Riccati equations of this type appear in applied probability and transport theory. The minimal nonnegative solution of these equations can be found by Newton’s method and basic fixed-point iterations. The study of these equations is also closely related to th...

We consider the numerical solution of differential Riccati equations. We review the existing methods and investigate whether they are suitable for large-scale problems arising in LQR and LQG design for semi-discretized partial differential equations. Based on this review, we suggest an efficient matrix-valued implementation of the BDF for differential Riccati equations.

Matrix Riccati equations and other nonlinear ordinary differential equations with superposition formulas are, in the case of constant coefficients, shown to have the same exact solutions as their group theoretical discretizations. Explicit solutions of certain classes of scalar and matrix Riccati equations are presented as an illustration of the general results. Typeset using REVTEX 1