Switching surfaces and null-controllable region of a class of LTI systems using Gröbner basis

@article{Patil2012SwitchingSA,
  title={Switching surfaces and null-controllable region of a class of LTI systems using Gr{\"o}bner basis},
  author={Deepak U. Patil and Debraj Chakraborty},
  journal={2012 IEEE 51st IEEE Conference on Decision and Control (CDC)},
  year={2012},
  pages={1279-1284}
}
The problem of time optimal feedback control of a single input, continuous time, linear time invariant (LTI) system is considered. The control input is constrained to obey |u(t)| ≤ 1. It is known that the solution to this problem is bang-bang with the input switching between the extreme values ±1 according to some “switching surfaces” in the state space. It is shown that for a class of LTI systems, these switching surfaces can be represented as semi-algebraic sets and a method to construct… CONTINUE READING