Stabilisability and stability for explicit and implicit polynomial systems: A symbolic computation approach

Stabilisability and stability for a large class of discrete-time polynomial systems can be decided using symbolic computation packages for quantifier elimination in the first order theory of real closed fields. A large class of constraints on states of the system and control inputs cart be treated i n the same way. Stability of a system can be checked by constructing a Lyap unov function, which is assumed to belong to a class of polynomial positive definite functions. Moreover, we show that stability/stabilisability can b e decided directly from the epsilon-delta definition.