Structured and simultaneous Lyapunov functions for system stability problems. (English) Zbl 0683.93057
Summary: It is shown that many system stability and robustness problems can be reduced to the question of when there is a quadratic Lyapunov function of a certain structure which establishes stability of \(\dot x=Ax\) for some appropriate A. The existence of such a Lyapunov function can be determined by solving a convex program. We present several numerical methods for these optimization problems. A simple numerical example is given.
MSC:
93Dxx | Stability of control systems |
93B40 | Computational methods in systems theory (MSC2010) |
93B35 | Sensitivity (robustness) |
65K05 | Numerical mathematical programming methods |