Displacement In Space Of The Equilibria Of Unstable Dissipative Systems
Luis Javier Onta˜n´on-Garc´ıa, Eric Campos Canton
Piecewise linear systems based on unstable dissipative systems (UDS) in R^3 consist of one of the two possible conditions regarding their eigenvalues.
The UDS of the type I, present a lambda_{1} real negative eigenvalue and two lambda_{2,3} complex conjugated valueswith real positive parts.
Since the trajectories formed by these systems are unbounded due to their stability, two or more subsystems need to be considered in order to restrain the resulting orbit generating self-sustained oscillations.
To do so, one must consider the intrinsic properties of the systems along with the location in space in which the equilibrium is located, in order to design switching control laws that bound the resulting trajectories.