Abstract. For linear time-invariant (LTI) state space systems it is well-known that its asymptotic stability can be related to solution properties of the Lyapunov matrix equation according to so-called inertia theorems. The question now arises how analogous results can be obtained for LTI descriptor systems (singular systems, differential-algebraic equations). The stability behaviour of a LTI d...

We present the first order error bound for the Lyapunov equation AX +XA∗ = −GG∗, where A is perturbed to A+ δA. We use the structure of the solution of the Lyapunov equation X = m ∑ k=1 WkW ∗ k , where Wk is the k-th matrix obtained by the Low Rank Cholesky Factor ADI (LRCF-ADI) algorithm using the set of ADI parameters equal to exact eigenvalues of A, that is with ADI parameters {p1, . . . , p...

This paper presents a new kind of recurrent neural network proposed by Zhang et al. for solving online Lyapunov equation with time-varying coefficient matrices. Global exponential convergence could be achieved by such a recurrent neural network when solving the timevarying problems in comparison with gradient neural networks (GNN). MATLAB simulation of both neural networks for the real-time sol...

In this paper a procedure for construction of complete type Lyapunov–Krasovskii functionals for a scalar neutral type time delay equation is considered. The construction of the functionals depends on the so-called Lyapunov functions which satisfy a delay equation with additional boundary conditions. It is shown that these functionals admit lower and upper quadratic bounds. Exponential estimates...

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...

We develop a general method for obtaining bounds for the sensitivity of the solution of the stable Lyapunov equation. Our arguments not only work simultaneously for both the continuous and the discrete time Lyapunov equations, they work equally well for more general equations that have been studied. Further, we obtain bounds valid for all unitarily invariant norms. x 1 Introduction In this note...