Stability radii and global stability of difference systems

A linear difference system with complex coefficients is considered. It is assumed that the coefficients of the system depend on some uncertain parameters. The stability of the system depends not only on the values of these parameters but also on the values of delays. There are situations that guarantee stability for all positive values of the delays. The authors gives some necessary and sufficient conditions for stability of the system for all admissible values of the uncertain parameters, which is preserved for all positive values of delays. The main tool is the complex stability radii of the matrix with respect to the unit disk of the complex plane. Some integral formulas for solutions of the system are given