In each case the simple manipulation of symbols according to explicit rules imparts upon the system the capacity to perform complex computations – in fact, given access to infinite memory and sufficient time, any computable function is calculable (i.e., any function that can be computed, is computable by the given system).
Then, by constructing certain new multiple time-varying Lyapunov functions, computable sufficient conditions for the global stabilization task are proposed within the framework of dwell-time switching.
When one has a sampled-data state feedback controller, which is designed according to an approximate discrete-time model and exponentially stabilizes the approximate discrete-time model, our result gives a computable sufficient condition to check if the sampled-data state feedback controller also exponentially stabilizes the continuous-time plant.
For example, the system defined above would be represented in the "Thue" programming language as *+*::= ** ::= *+**+***+**** Despite its simplicity, the semi-Thue formalism is nevertheless known to be Turing complete., Thus, given infinite memory and sufficient time, any computable function is calculable using such systems.
On the other hand, systems biologists rarely stay the course with the two book-length expositions of relational biology [ 6, 7], and may even believe that anything is computable, given sufficient time and processing power, despite the fact that computer scientists have long known this to be trivially false [ 14].
However, by considering the same systems with unknown but bounded exogenous disturbances, we give finitely computable conditions, sufficient for stabilizability without disturbances, yet necessary for stabilizability with disturbances.
These instruments represent computable necessary and sufficient conditions for the existence of the properties (i), (ii), and whenever the property (ii) exists, a suitable state-feedback matrix is provided.
For (u,t) in the open cone determined by 0<|u|<t<2|u|, we first prove that the algebraic variety has exactly 7 points and rankM 3)="7; we then apply the above mentioned result to obtain a concrete, computable, necessary and sufficient condition for the existence of a representing measure.
They presented the notion of connectivity robustness based on inter-vehicle distances, which can generate a locally computable function providing a sufficient reference for connectedness of the network.
The granularity of the model was limited to a sufficient level of details that makes it computable.
