We study the general discrete-time algebraic Riccati equation and deal with the case where the closed loop matrix corresponding to an arbitrary solution is singular. In this case the extended symplectic pencil associated with the DARE has 0 as a characteristic root and the corresponding spectral deflating subspace gives rise to a subspace where all solutions of the DARE coincide. This allows fo...

We consider the infinite horizon quadratic cost minimization problem for a linear system with finitely may inputs and outputs. A common approach to treat a problem of this type is to construct a semigroup in an abstract state space, and to use infinite-dimensional control theory. However, this approach is less appealing in the case where there are discrete time delays in the impulse response, b...

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...

This paper is concerned with a discrete-time indefinite stochastic LQ problem in an infinite-time horizon. A generalized stochastic algebraic Riccati equation GSARE that involves the MoorePenrose inverse of a matrix and a positive semidefinite constraint is introduced. We mainly use a semidefinite-programmingSDPbased approach to study corresponding problems. Several relations among SDP compleme...

We study the problem of existence of weak right or left or strong coprime factorizations in H-infinity over the right half-plane of an analytic function defined in some subset of the right half-plane. We give necessary and sufficient conditions for the existence of such coprime factorizations in terms of an optimal control problem over the doubly infinite continuous-time axis. In particular, we...

Abstract. We define a new class of solutions to the WDVV associativity equations. This class is determined by the property that one of the commuting PDEs associated with such a WDVV solution is linearly degenerate. We reduce the problem of classifying such solutions of the WDVV equations to the particular case of the so-called algebraic Riccati equation and, in this way, arrive at a complete cl...

In this paper, new upper matrix bounds for the solution of the continuous algebraic Riccati equation (CARE) are derived. Following the derivation of each bound, iterative algorithms are developed for obtaining sharper solution estimates. These bounds improve the restriction of the results proposed in a previous paper, and are more general. The proposed bounds are always calculated if the stabil...

Linear quadratic controllers for dynamical systems with complicated dynamics are presented. Systems with complicated dynamics are those that run over compact sets and have such features as nontrivial recurrence, periodic and aperiodic orbits. The controllers are based on modeling the nonlinear dynamical systems as linear dynamically varying systems. Necessary and sufficient conditions for the e...

We first obtain by analogy with the continuous (differential) case the general solution of the discrete Riccati equation. Moreover, we establish the full equivalence between our discrete Riccati equation and a corresponding homogeneous second order discrete linear equation. Our results can be considered the discrete analog of Mielnik's construction in supersymmetric quantum mechanics [J. Math. ...