### Citations

187 | Tsitsiklis. A survey of computational complexity results in systems and control
- Blondel, N
(Show Context)
Citation Context ...ost control problems are not clearly understood. The computational complexity of stability properties has been a topic of much recent investiga1http://dreal.cs.cmu.edu 2http://github.com/dreal 6 tion =-=[3, 4, 5, 1, 16, 2]-=-. A focus of existing work is to establish various hardness results, i.e., lower bounds on complexity. It is shown that stability of simple systems is hard or impossible to solve algorithmically. Such... |

57 | Tsitsiklis, “Complexity of stability and controllability of elementary hybrid systems
- Blondel, N
- 1999
(Show Context)
Citation Context ...ost control problems are not clearly understood. The computational complexity of stability properties has been a topic of much recent investiga1http://dreal.cs.cmu.edu 2http://github.com/dreal 6 tion =-=[3, 4, 5, 1, 16, 2]-=-. A focus of existing work is to establish various hardness results, i.e., lower bounds on complexity. It is shown that stability of simple systems is hard or impossible to solve algorithmically. Such... |

21 | Delta-complete decision procedures for satisfiability over the reals. In
- Gao, Avigad, et al.
- 2012
(Show Context)
Citation Context ...1| ≤ δ3 ) is what really matters in practice, for some choices of numerical error bounds δ1, δ2, δ3 ∈ Q +. Formalizing this observation, we have developed the theory of delta-decisions over the reals =-=[8, 7]-=-. In this new theory we relax the standard decision problem to ask whether a sentence is true or its “delta-strengthening” is false. Namely, we allow one-sided, delta-bounded numerical errors in logic... |

9 | Algebraic relaxations and hardness results in polynomial optimization and Lyapunov analysis
- Ahmadi
- 2011
(Show Context)
Citation Context ...s, absolute value, and solution functions of Lipschitz-continuous ordinary differential equations. The complexity of Type 2 computable functions is also well studied. Intuitively, a real function f : =-=[0, 1]-=- → R is (uniformly) P-computable (PSPACE-computable), if it is computable by an oracle Turing machine Mf that halts in polynomial-time (polynomial-space) for every i ∈ N and every ~x ∈ dom(f). We deno... |

6 | Complexity of ten decision problems in continuous time dynamical systems, - Ahmadi, Majumdar, et al. - 2013 |

2 | Stability of polynomial differential equations: Complexity and converse lyapunov questions
- Ahmadi, Parrilo
(Show Context)
Citation Context ...ost control problems are not clearly understood. The computational complexity of stability properties has been a topic of much recent investiga1http://dreal.cs.cmu.edu 2http://github.com/dreal 6 tion =-=[3, 4, 5, 1, 16, 2]-=-. A focus of existing work is to establish various hardness results, i.e., lower bounds on complexity. It is shown that stability of simple systems is hard or impossible to solve algorithmically. Such... |