H∞ sampled data control of systems with time-delays

Sampled-data Hinfin control of linear systems with state, control and measurement constant delays is considered. The sampling of the controlled input and of the measured output is not assumed to be uniform. The system is modelled as a continuous-time one, where the controlled input and the measurement output have piecewise-continuous delays. The input-output approach to stability and L₂-gain analysis is applied to the resulting system. The discretized Lyapunov functional method is extended to the case of multiple delays, where the Lyapunov functional is complete in one of the delays (in the state) and is simple in the other delays (in the input and in the output), which are unknown, time-varying with known upper-bounds. Solutions to the state-feedback and the output- feedback Hinfin control problems are derived in terms of linear matrix inequalities (LMIs).