Mw. Mcconley et al., COMPUTATIONAL-COMPLEXITY OF LYAPUNOV STABILITY ANALYSIS PROBLEMS FOR A CLASS OF NONLINEAR-SYSTEMS, SIAM journal on control and optimization (Print), 36(6), 1998, pp. 2176-2193
Citations number
32
Categorie Soggetti
Mathematics,"Robotics & Automatic Control",Mathematics,"Robotics & Automatic Control
Nonlinear control systems can be stabilized by constructing control Ly
apunov functions and computing the regions of state space over which s
uch functions decrease along trajectories of the closed-loop system un
der an appropriate control law. This paper analyzes the computational
complexity of these procedures for two classes of control Lyapunov fun
ctions. The systems considered are those which are nonlinear in only a
few state variables and which may be affected by control constraints
and bounded disturbances. This paper extends previous work by the auth
ors, which develops a procedure for stability analysis for these syste
ms whose computational complexity is exponential only in the dimension
of the ''nonlinear'' states and polynomial in the dimension of the re
maining states. The main results are illustrated by a numerical exampl
e for the case of purely quadratic control Lyapunov functions.