Closed-loop stability analysis of a linear matrix inequalities based reduced multiple-model control algorithm

• Published in: International journal of dynamics and control Vol. 12; no. 7; pp. 2341 - 2350
• Main Authors: Rikhtehgar, Pouya, Haeri, Mohammad
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2024; Springer Nature B.V
• Subjects: Algorithms; Closed loops; Complexity; Control; Control algorithms; Control and Systems Theory; Control theory; Controllers; Decomposition; Dynamical Systems; Engineering; Linear matrix inequalities; Nonlinear control; Nonlinear systems; Nonlinearity; Stability analysis; Systems analysis; Vibration; Stability margin; Linear matrix inequality; Stability analysis; Model order reduction; Multiple-models; Gap metric
• ISSN: 2195-268X; 2195-2698
• DOI: 10.1007/s40435-023-01354-8

Reduced multiple-model control design as an alternative approach to control complex nonlinear systems could bring about the simplicity in system analysis, control design, and implementation and could guarantee the local stability using two tools: gap metric and stability margin. This is while a study on closed-loop stability of nonlinear systems remains a contentious issue which is left to be solved. We introduced a stability analysis of a linear matrix inequalities based reduced multiple-model control algorithm, whereby the closed-loop stability will be met driven via Lyapunov approach. The stabilizing strategy is applied to design a reduced multiple-model control using linear matrix inequality. The global stability could be guaranteed via such a valuable approach. This is illustrated on a complex nonlinear system, which is modeled around two different operating points to describe its strong nonlinearities. The closed-loop stability properties are also illustrated via computer simulations.