A linear matrix inequality (LMI) approach to robust H/sub 2/ sampled-data control for linear uncertain systems.
Li-Sheng Hu1, J Lam, Yong-Yan Cao
1Dept. of Autom., Shanghai Jiao Tong Univ., China.
Summary
This study introduces robust optimal control for uncertain linear systems using H2 sampled-data control. It presents new methods for multirate systems and stability analysis, improving upon traditional techniques.
Area of Science:
- Control Theory
- Systems Engineering
- Applied Mathematics
Background:
- Uncertain linear systems pose challenges for traditional control methods.
- H2 norm is a key performance metric in control system analysis.
- Sampled-data control introduces complexities due to discrete-time implementation.
Purpose of the Study:
- To develop robust optimal control strategies for uncertain linear systems using H2 sampled-data control.
- To address multirate sampled-data control design for periodic time-varying systems.
- To establish a new stability criterion for hybrid systems.
Main Methods:
- Utilizing the impulse response interpretation of the H2 norm.
- Developing two distinct H2 measures for sampled-data systems.
- Formulating control design as an optimization problem solvable via linear matrix inequalities.
- Establishing a novel stability result for hybrid systems.
Main Results:
- Proposed robust optimal control procedures for uncertain linear systems under two H2 criteria.
- Presented a multirate, periodic time-varying robust optimal control framework.
- Derived a new stability condition for hybrid systems, applicable to single-rate and multirate cases.
- Explicitly incorporated the sampling period into the control design results.
Conclusions:
- The proposed H2 sampled-data control methods offer a robust approach for uncertain linear systems.
- The developed techniques, particularly for multirate systems, provide superior performance by explicitly considering the sampling period.
- The new stability result for hybrid systems facilitates advanced control design for complex systems.
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