Absolute stability of nonautonomous delay systems: delay-dependent and delay-independent criteria

This paper deals with the problem of absolute stability for multivariable systems with time-varying memoryless nonlinearities subject to sector conditions, and with delays. Assuming essentially a sector condition on the rate of variation of the nonlinearities, we provide two different types of stability criteria. 1. A frequency criterion extends the Popov criterion to systems with time-varying nonlinearities, and leads to simple graphical interpretations for scalar systems. For rational transfers, the main required condition is equivalent to a linear matrix inequality (LMI) :this furnishes a tractable method of numerical resolution by approximation. 2. A delay-independent criterion is given, expressed as an LMI condition. Both approaches lead to local and global stability results. A numerical example of an application is treated.