LMIs in Control/pages/CT-SOFS
LMIs in Control/pages/CT-SOFS
In view of applications, static feedback of the full state is not
feasible in general: only a few of the state variables (or a linear
combination of them,
, called the output) can be
actually measured and re-injected into the system.
So, we are led to the notion of static output feedback
The System
[edit | edit source]Consider the continuous-time LTI system, with generalized state-space realization
The Data
[edit | edit source]The Optimization Problem
[edit | edit source]This system is static output feedback
stabilizable (SOFS) if there exists a matrix
F such that the closed-loop system
(obtained by replacing which means applying static output feedback)
is asymptotically stable at the origin
The LMI: LMI for Continuous Time - Static Output Feedback Stabilizability
[edit | edit source]The system is static output feedback stabilizable if and only if it satisfies any of the following conditions:
- There exists a and , where , such that
- There exists a and , where , such that
- There exists a and , where , such that
- There exists a and , where , such that
Conclusion
[edit | edit source]On implementation and optimization of the above LMI using YALMIP and MOSEK (or) SeDuMi we get 2 output matrices one of which is the Symmeteric matrix (or ) and
Implementation
[edit | edit source]A link to the Matlab code for a simple implementation of this problem in the Github repository:
https://github.com/yashgvd/LMI_wikibooks
Related LMIs
[edit | edit source]Discrete time Static Output Feedback Stabilizability
Static Feedback Stabilizability
External Links
[edit | edit source]- [1] - LMI in Control Systems Analysis, Design and Applications
- LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
- LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.
- D. d. S. Madeira and J. Adamy, "Static output feedback: An LMI condition for stabilizability based on passivity indices," 2016 IEEE Conference on Control Applications (CCA), Buenos Aires, 2016, pp. 960-965.