题目: A Delay Decomposition Approach to Stability and H-infinity Control of Linear Time-Delay Systems
摘要: This presentation includes two parts. The first part considers the problem of stability of linear time-delay systems. Firstly, a delay decomposition approach is proposed to deal with the problem. The idea of the approach is that the delay interval is uniformly divided into N segments with N a positive integer, and a proper Lyapunov-Krasovskii functional is chosen with different weighted matrices corresponding to different segments in the Lyapunov-Krasovskii functional. Secondly, based on the delay decomposition approach, some new delay-dependent stability criteria for linear time-delay systems are derived. These criteria are much less conservative and include some existing results as their special cases. Numerical examples show that significant improvement using the delay decomposition approach is achieved over some existing method even for coarse delay decomposition. For fine delay decomposition, the delay limit for stability can be approached.
The second part is concerned with H-infinity control for linear time-delay systems. Delay-dependent bounded real lemmas (BRLs) are established by using a delay decomposition approach. Employing the obtained BRLs, some delay-dependent sufficient conditions for the existence of memoryless and delayed state feedback controllers, which ensure asymptotic stability and a prescribed H-infinity performance level of the corresponding closed-loop system, is formulated in terms of a linear matrix inequality (LMI). A practical example is given to illustrate the effectiveness of the design method.
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