# zbMATH — the first resource for mathematics

Reachability in variable structure control systems. (English) Zbl 0541.93004
In controlled systems there exists a class of systems with discontinuous control of the sliding mode type. These systems are interesting as for them the usual premises guaranteeing the existence of solutions fail to hold. They are important in applications: Under some feasible conditions they guarantee good dynamical properties despite unknown controlled parameters and unmeasured disturbances. The authors are concerned with a subclass of systems $$\dot x=(A-k^ T+\Delta k^ T)x,$$ where the fixed feedback gain k is used to guarantee the conditions for switching the gain vector $$\Delta$$ k which is switched dynamically to obtain the sliding regime both for full $$\Delta$$ k switching and for some components of $$\Delta$$ k switching. After deriving the conditions for the state order n, a detailed example for order 3 is presented.
Reviewer: A.Vaněček

##### MSC:
 93B05 Controllability 49J30 Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) 93C99 Model systems in control theory 93B03 Attainable sets, reachability
##### Keywords:
discontinuous control; sliding mode; feedback gain; switching
Full Text: