LMIs in Control/pages/Unsat Inp Stabilization

From Wikibooks, open books for an open world
Jump to navigation Jump to search

LMI For Stabilization Condition for Systems With Unsymmetrical Saturated Control

The LMI in this page gives the feasibility conditions which, if satisfied, imply that the correstponding system can be stabilized.

The System[edit | edit source]

where is the state, is the control input.

For the system given as above, its symmetrical saturated control form can be derived by following the procedure in the original article. The new system will have the form:


The Data[edit | edit source]

The system matrices , the saturation bounds of the control inputs. Positive scalars .

The LMI: The Stabilization Feasibility Condition[edit | edit source]

Here is a diagonal matrix with a component either 0 or 1, and and

Conclusion:[edit | edit source]

The feasibility of the given LMI implies that the system is stabilizable with control gains .

Implementation[edit | edit source]

A link to CodeOcean or other online implementation of the LMI

Related LMIs[edit | edit source]

External Links[edit | edit source]

Return to Main Page:[edit | edit source]