Stability and L2-Gain Analysis of Systems with Time-Varying Delays: Input-Output Approach

Stability and L2(l2)-gain analysis of linear (continuous-time and discrete-time) systems with uncertain bounded time-varying delays possessing non-zero nominal values and norm-bounded uncertainties. The delay derivatives (in the continuous-time) are not assumed to be less than q < 1. An input-output approach is applied by introducing a new input-output model, which leads to effective frequency domain and time domain criteria. The new method essentially improves the existing results for delays with derivative not greater than 1, which were treated in the past as fast-varying delays (without any constraints on the delay derivative). New BRLs are derived for systems with state and objective vector delays. Numerical examples illustrate the efficiency of the new method.