## What is/are Coupled Lyapunov?

Coupled Lyapunov - An improved successive over-relaxation iterative method is proposed for coupled Lyapunov matrix equations (CLMEs) from continuous-time Markovian jump linear systems.^{[1]}This study investigates gradient-based neural networks (GNNs) for solving coupled Lyapunov matrix equations arising in the stability analysis of continuous-time Markovian jump linear systems.

^{[2]}Finally, we obtain coupled Lyapunov systems of linear equations, which are analyzed by the MATLAB solver for the system.

^{[3]}This paper is concerned with the methods for solving continuous coupled Lyapunov matrix equations.

^{[4]}It is shown that the system controlled by RHC is stabilizable if and only if the two coupled Lyapunov type inequalities are satisfied.

^{[5]}The new state estimation is derived via the innovation analysis method, and an analytical solution to the estimator is given in terms of a set of generalised Riccati difference equations based on a set of coupled Lyapunov equations.

^{[6]}First, for a general stochastic system with input delay and multiplicative noises, we derive a necessary stabilizing condition based on a coupled Lyapunov equation (CLE).

^{[7]}ABSTRACT In this paper, a new gradient-based iterative algorithm is proposed to solve the coupled Lyapunov matrix equations associated with continuous-time Markovian jump linear systems.

^{[8]}Especially, a novel stability criterion is developed for the considered systems by the existence of the unique positive-definite solution of the corresponding coupled Lyapunov matrix equations.

^{[9]}

## coupled lyapunov matrix

An improved successive over-relaxation iterative method is proposed for coupled Lyapunov matrix equations (CLMEs) from continuous-time Markovian jump linear systems.^{[1]}This study investigates gradient-based neural networks (GNNs) for solving coupled Lyapunov matrix equations arising in the stability analysis of continuous-time Markovian jump linear systems.

^{[2]}This paper is concerned with the methods for solving continuous coupled Lyapunov matrix equations.

^{[3]}ABSTRACT In this paper, a new gradient-based iterative algorithm is proposed to solve the coupled Lyapunov matrix equations associated with continuous-time Markovian jump linear systems.

^{[4]}Especially, a novel stability criterion is developed for the considered systems by the existence of the unique positive-definite solution of the corresponding coupled Lyapunov matrix equations.

^{[5]}

## coupled lyapunov equation

The new state estimation is derived via the innovation analysis method, and an analytical solution to the estimator is given in terms of a set of generalised Riccati difference equations based on a set of coupled Lyapunov equations.^{[1]}First, for a general stochastic system with input delay and multiplicative noises, we derive a necessary stabilizing condition based on a coupled Lyapunov equation (CLE).

^{[2]}