Abstract
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 can be treated in the same way. Stability of a system can be checked by constructing a Lyapunov function, which is assumed to belong to a class of polynomial positive definite functions. Moreover, we show that stability/ stabilisability can be decided directly from the e-δ definition.
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