Linear Matrix Inequalities in Control

Optimiser: SeDuMi
Demo no.11
Preprocesor: YALMIP
For the plant with measurable, time-varying parameter a
design the gain scheduling controller.
1
G( s)
; a 1.0
s(
s a)
1.0
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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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Conclusions
• New (~15 years old) control analysis and control synthesis
tool,
• Active field of research with many unsolved problems:
– BMI as natural formulation of control problems,
but not convex,
– suboptimal, low order controllers, controllers with structure (nonsmooth,
non-convex algorithms).
– output controllers for uncertain plants,
– synthesis for systems with delays, saturations,
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