The general common nonnegative-definite and positive-definite solutions to the matrix equations AXA∗ = BB∗ and CXC∗ = DD∗

AbstractWe give necessary and sufficient conditions for the existence of a common nonnegative-definite (positive-definite) solution to the pair of matrix equations AXA∗ = BB∗ and CXC∗ = DD∗, and derive a representation of the general common nonnegative-definite (positive-definite) solution to these two equations when they have such common solutions. This paper can be viewed as a supplementary version of that derived by Young et al. [1] since Groβ [2] has given a counterexample to point out a mistake in their basic Theorem 1. The presented example shows the advantage of the proposed approach

Gateway design for LAN interconnection via ISDN

Computer Networks and ISDN Systems19143-5

A Less Conservative Stability Criterion for Delayed Stochastic Genetic Regulatory Networks

This paper concerns the problem of stability analysis for delayed stochastic genetic regulatory networks. By introducing an appropriate Lyapunov-Krasovskii functional and employing delay-range partition approach, a new stability criterion is given to ensure the mean square stability of genetic regulatory networks with time-varying delays and stochastic disturbances. The stability criterion is given in the form of linear matrix inequalities, which can be easily tested by the LMI Toolbox of MATLAB. Moreover, it is theoretically shown that the obtained stability criterion is less conservative than the one in W. Zhang et al., 2012. Finally, a numerical example is presented to illustrate our theory