Robust control using nonlinear dynamic state-feedback

MATLAB code for the example in Ref.¹. We use MATLAB with YALMIP ² and MOSEK ³.

File(s)

This repository includes the following MATLAB files:

1- Example of a two-wheeled inverted pendulum mobile platform: Example.m.

2,3,4- Construction of the nonlinear dynamic feedback law: f_fun.m, g_fun.m, & phi_fun.m.

5- Finding the vertices of a polytopic set of matrices: vertices.m

6- Choosing an element within a polytopic set: sys_eval_box.m.

7- Finding the vertices of a polytopic set of matrices: qs_vertices.m.

8- Covering a polytopic set of systems with a finite number of quadratically stabilizable subsets: setcover.m.

License(s)

MIT

Footnotes

1. Shakouri, A., Heidema, M., van Waarde, H.J., 2026. Robust stabilization of discrete-time linear systems requires nonlinear dynamic feedback. arXiv:2608.19010. ↩

2. Lofberg, J., 2004. YALMIP : A Toolbox for Modeling and Optimization in MATLAB. In Proceedings of the CACSD Conference. ↩

3. MOSEK ApS, 2026. The MOSEK Python Fusion API manual. Version 11.0. ↩