We investigate here the numerical solution of a special type of descriptor continuous-time Riccati equation which is involved in solving several key problems in robust control, formulated under very general hypotheses. We also give necessary and sufficient existence conditions together with computable formulas for both stabilizing and antistabilizing solutions in terms of the associated matrix ...

The low-and-high gain design technique, which was initiated in 10] for a chain of integrators and completed in 13] for general linear asymptotically null controllable with bounded controls systems, was conceived for semi-global control problems beyond stabilization and was related to the performance issues such as semi-global stabilization with enhanced utilization of the available control capa...

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.

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...

Normwise backward errors and residual bounds for an approximate Hermitian positive semidefinite solution set to the periodic discrete-time algebraic Riccati equation are obtained. The results are illustrated by using simple numerical examples.

Let H and Y be separable Hilbert spaces, U finite dimensional. Let A ∈ L(H), B ∈ L(U, H), C ∈ L(H,Y ), D ∈ L(U,Y ), and suppose that the open loop transfer function D(z) := D + zC(I − zA)B ∈ H∞(U, Y ). Let J ≥ 0 be a cost operator. We study a subset of self adjoint solutions P of the discrete time algebraic Riccati equation (DARE)

In this paper, we consider a robust stability problem for continuous time stochastic uncertain systems. The uncertainty in the system is characterized in terms of an uncertain probability distribution on the noise input. This uncertainty is assumed to satisfy a certain relative entropy constraint. The solution to a specially parametrized risk-sensitive performance analysis problem is used to es...