Control systems theory
Stability Analysis of Nonlinear Quadratic Systems via Polyhedral Lyapunov Functions
Quadratic systems play an important role in the modeling
of a wide class of nonlinear processes (electrical,
robotic, biological, etc.). For such systems it is of
mandatory importance not only to determine whether the
origin of the state space is locally asymptotically stable,
but also to ensure that the operative range is included
into the convergence region of the equilibrium.
Based on this observation, this research considers the
following problem: given the zero equilibrium point of a
nonlinear quadratic system, assumed to be locally
asymptotically stable, and a certain polytope in the state
space containing the origin, determine whether this
polytope belongs to the region of attraction of the
equilibrium. The proposed approach is based on polyhedral
Lyapunov functions, rather than on the classical quadratic
Lyapunov functions. An example shows that our methodology
may return less conservative results than those obtainable
with previous approaches.