Controllable Hopf bifurcations of codimension 1 and 2 in nonlinear control systems

• Published in: Nonlinear analysis Vol. 74; no. 9; pp. 3046 - 3054
• Main Authors: Braga, Denis de Carvalho, Mello, Luis Fernando, Rocşoreanu, Carmen, Sterpu, Mihaela
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 01-06-2011; Elsevier
• Subjects: Bautin bifurcation; Control system; Control systems; Design engineering; Exact sciences and technology; Global analysis, analysis on manifolds; Hopf bifurcation; Mathematical analysis; Mathematics; Nonlinearity; Orbits; Orientation; Periodic orbit; Scalars; Sciences and techniques of general use; Stability; State feedback; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; 47N70; Stability; 34D20; Control system; Bautin bifurcation; Periodic orbit; Hopf bifurcation; 37G15; Nonlinear analysis; Mathematical model; Non linear system; Numerical stability
• ISSN: 0362-546X; 1873-5215
• DOI: 10.1016/j.na.2011.01.033

The purpose of this work, given a nonlinear control system, is to design a four-parameter family of static state feedback such that the corresponding closed-loop control system exhibits controllable Hopf bifurcations of codimension 1 and 2. More precisely, the scalar law designed by us permits the control of the stability of the equilibrium points and the orientation and stability of the periodic orbits.