The purpose of this paper is to investigate the role that the continuous-time generalised Riccati equation plays within the context of singular linear-quadratic optimal control. This equation has been defined following the analogy with the discrete-time generalised Riccati equation, but, differently from the discrete case, to date the importance of this equation in the context of optimal contro...

Linear dynamically varying H∞ controllers are developed for tracking natural trajectories of a broad class of nonlinear systems defined over compact sets. It is shown that the existence of a suboptimal H∞ controller is related to the existence of a bounded solution to a functional algebraic Riccati equation. Even though nonlinear systems running over compact sets could exhibit sensitive depende...

Linear closed-loop no-memory strategies for the LQ Nash game are considered. We exhibit a class of such problems with the property that the solution exists for any finite time interval; for the infinite time case, there exist none or a unique or many solutions, depending on the choice of the parameters. In addition, the limit of the finite time solution as the time interval increases does not h...

In this paper a very general matrix quadratic equation is considered. This equation is known in literature as asymmetric Algebraic Riccati Equation (ARE) and arises in the solution of many problems in system and control theory and applied mathematics. For this reason a large amount of work has been produced on this topic. We present a new parametrization of the set of solutions of such equation...

Algebraic Riccati equations with indefinite quadratic terms play an important role in applications related to robust controller design. While there are many established approaches solve these case of small-scale dense coefficients, is no approach available compute solutions the large-scale sparse setting. In this paper, we develop iterative method low-rank approximations stabilizing continuous-...

In most H2 and H∞ control problems solutions of the algebraic Riccati equation play a crucial role. Note that in general for continuous time systems we have to use quadratic matrix inequalities instead of Riccati equations. For details we refer to [5]. In particular we are interested in the stabilizing solution of these Riccati equations and quadratic matrix inequalities. However, if the system...

The optimal control problem in a finite time horizon with an indefinite quadratic cost function for a linear system subject to multiplicative noise on both the state and control can be solved via a constrained matrix differential Riccati equation. In this paper, we provide general necessary and sufficient conditions for the solvability of this generalized differential Riccati equation. Furtherm...

Algebraic geometry plays an important role in the theory of linear systems for (at least) three reasons. First, the Laplace transform turns expressions about linear differential systems into expressions involving rational functions. In addition, many of the transformations studied in linear systems theory, like changes of coordinates or feedback, turn out to be the action of algebraic groups on...

In this paper, we study the existence of solutions to a degenerate algebraic Riccati equation associated to an optimal control problem with infinite time horizon. Under some assumptions on the control system, we can select a solution to this Riccati equation providing a feedback control law able to stabilize the system.