We model the behaviour of a relativistic spherically symmetric shearing fluid undergoing gravitational collapse with heat flux. It is demonstrated that the governing equation for the gravitational behaviour is a Riccati equation. We show that the Riccati equation admits two classes of new solutions in closed form. We regain particular models, obtained in previous investigations, as special case...

This paper presents a new detectability concept for discretetime Markov jump linear systems with finite Markov state, which generalizes the MS-detectability concept found in the literature. The new sense of detectability can similarly assure that the solution of the coupled algebraic Riccati equation associated to the quadratic control problem is a stabilizing solution. In addition, the paper i...

We study the matrix equation XA − AX = X p in M n (K) for 1 < p < n. It is shown that every matrix solution X is nilpotent and that the generalized eigenspaces of A are X-invariant. For A being a full Jordan block we describe how to compute all matrix solutions. Combinatorial formulas for A m X ℓ , X ℓ A m and (AX) ℓ are given. The case p = 2 is a special case of the algebraic Riccati equation.

The problem of the continuous-time H∞ fixed-lag smoothing over the infinite horizon is studied. The first solution to the problem is derived in terms of one algebraic Riccati equation of the same dimension as in the filtering case and the mechanism by which the performance improvements with respect to the H∞ filtering occur is clarified. It is shown that the H∞ smoother exploits the information...

This paper is devoted to the perturbation analysis for the periodic discrete-time algebraic Riccati equations (P-DAREs). Perturbation bounds and condition numbers of the Hermitian positive semidefinite solution set to the P-DAREs are obtained. The results are illustrated by numerical examples.

In this paper we construct infinitely many selfadjoint solutions of the control algebraic Riccati equation using invariant subspaces of the associated Hamiltonian. We do this under the assumption that the system operator is normal and has compact inverse, and that the Hamiltonian possesses a Riesz basis of invariant subspaces.

We study the solutions of the discrete time algebraic Riccati equation for stable linear systems. We give sharpened existence results for such solutions (in comparison to our earlier work [4]) under an extra assumption that makes the state space isomorphism techniques applicable. This extends some of the known results on the parameterization of stable spectral factors for realizations with infi...

This paper presents a survey of some new applications of algebraic Riccati equations. In particular, the paper surveys some recent results on the use of algebraic Riccati equations in testing whether a system is negative imaginary and in synthesizing state feedback controllers which make the closed loop system negative imaginary. The paper also surveys the use of Riccati equation methods in the...

Contrary to the continuous-time case, a discrete-time process y can be represented by minimal linear models (see (1.1) below), which may either have a non-singular or a singular D matrix. In fact, models with D = 0 have been commonly used in the statistical literature. On the other hand, for models with a singular D matrix the Riccati difference equation of Kalman filtering involves in general ...

• We often approximate a large number of periods, even if the horizon is known and finite, by assuming an infinite number of periods, and hope that this assumption will simplify the solution. Indeed, even if the general theory becomes more involved, the solution obtained often is simpler and has important computational and conceptual advantages: in particular, the optimal policy is often statio...