Linear Matrix Inequalities in Control

Scope of the lecture
• Control – classical vs. modern
• Optimisation approach
• Computer tools support
• LMI primer
• Basic LMI tools for control
• Analysis
• Synthesis
• Conclusions
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Synthesis (1)
What can be done within LMI framework?
• Design of static, state controller for uncertain
plants with H 2 /H inf norm minimization, pole
placement,
• Design of dynamic, output controller for nominal
plants with H 2 /H inf norm minimization, pole
placement,
• Design of dynamic, output controller for uncertain
plants with H 2 /H inf norm minimization, pole
placement, if uncertainity measurment is available
(so called gain-scheduling).
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Synthesis (2)
Typical strategy
Pole placement and H inf +H 2 norms minimisation,
• Select the pole placement region and run the test to
check, if it is feasible,
• Minimise H inf norm to find the smallest possible one
and controller,
• For several, greater but fixed values of H inf norm
minimise H 2 norms,
• Plot H 2 norms versus H inf fixed norms (Pareto like
curve),
• Select trade-off point or discard the design.
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