Quantifier Elimination and Semi-Algebraic Systems in Control

Parameter space design of control systems has a long tradition because of its advantage without losing degree of freedom in the system design. Parameters can stand for parametric uncertainties as well as controller parameter. Efficient implementations of symbolic computation with computer algebra tools presents an important research aspect for the analysis and design of control systems. The goal follows this line by formulating algebraic condition to the system stability and then applying more efficient semi-algebraic techniques to compute the stability region of system in parameter space.

• Formulate algebraic condition to the stability of parametric linear systems, including time-continuous, time-discrete, descriptor systems and switched systems.
• Implement quantifier elimination method to compute the stability region of parametric systems.
• Derive the existence condition of common Lyapunov function from the viewpoint of algebraic geometry and compute the feasible region of common Lyapunov function in the parameter space.
• Characterize the solvable condition to the parametric Riccati equation in control of linear systems based on algebraic geometry approach.
  
  

Computation of Feasible Parametric Regions for Common Quadratic Lyapunov Functions.
In Proceedings of the 17th European Control Conference, Cyprus (2018).
J. Tong, N. Bajcinca.
 
Computation of Feasible Parametric Regions for Lyapunov Functions.
11th Asian Control Conference (ASCC), Gold Coast (2017).
J. Tong, N. Bajcinca.
 
Stability Bounds for Systems and Mechanisms in Linear Descriptor Form.
Ilmenau Scientific Colloquium, 11.–15 (2017).
R. Voßwinkel, J. Tong, K. Robenack, N. Bajcinca.

Quantifier elimination
Algebraic geometry
Linear matrix inequality

Prof. Dr.-Ing. Naim Bajcinca
Gottlieb-Daimler-Str. 42
67663, Kaiserslautern
Phone: +49 631/205-3230
Fax: +49 631/205-4201
naim.bajcinca(at)mv.uni-kl.de

State of Rhineland-Palatinate

Since 2017

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