On the stability and control of the Schimizu-Morioka system of dynamical equations. (English) Zbl 1205.37023
The paper describes a local stability analysis for the three equilibrium points of a three-dimensional continuous-time dynamical system with quadratic dynamics resembling the Lorenz system. The authors use a standard linear eigenvalue analysis around the three equilibrium points and conclude that they are all unstable. One of them is not locally controllable whereas the remaining two others are locally controllable, so the authors propose an elementary stabilizing control strategy illustrated by simulations.
Reviewer: Didier Henrion (Toulouse)
MSC:
37B25 | Stability of topological dynamical systems |
37C10 | Dynamics induced by flows and semiflows |
37M20 | Computational methods for bifurcation problems in dynamical systems |
93C10 | Nonlinear systems in control theory |
93C15 | Control/observation systems governed by ordinary differential equations |