On Performance Analysis of Time Delay Systems using a Switched System Approach

The presence of a bounded time-varying delay in discrete-time controlled system implies a deterioration of the performance (stability and guaranteed cost). This paper studies controllers design for such a system, leading to a stabilized controlled system and to an upper bound of guaranteed cost as small as possible. The two contexts of state or only output availability are considered. These controllers are obtained via optimization algorithms using Linear Matrix Inequalities and Lyapunov-Krasovskii functions approach. An example illustrates the main results.