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Nonlinear dynamic system and built environment – basic premises

Bil J. S.

Przestrzeń i Forma

2016

nr 28

25--38

The system of impact of an object of architecture is a non-linear dynamic system, which also makes it a chaotic deterministic system. If we introduce into the system all impacts and system agent functions possible to identify, we can propose an estimated simulation of the life cycle of the entire object over time.

Układ oddziaływań obiektu jest nielinearnym układem dynamicznym, więc jest chaotycznym układem deterministycznym. Wprowadzając do systemu wszystkie możliwe do zdefiniowania oddziaływania i funkcje agentów systemu, można w przybliżeniu uzyskać symulację życia całego obiektu.

An approach to the analysis of observability and controllability in nonlinear systems via linear methods

Zhirabok A., Shumsky A.

International Journal of Applied Mathematics and Computer Science

2012

Vol. 22, no. 3

507-522

The paper is devoted to the problem of observability and controllability analysis in nonlinear dynamic systems. Both continuous- and discrete-time systems described by nonlinear differential or difference equations, respectively, are considered. A new approach is developed to solve this problem whose features include (i) consideration of systems with non-differentiable nonlinearities and (ii) the use of relatively simple linear methods which may be supported by existing programming systems, e.g.,Matlab. Sufficient conditions are given for nonlinear unobservability/uncontrollability analysis. To apply these conditions, one isolates the linear part of the system which is checked to be unobservable/uncontrollable and, if the answer is positive, it is examined whether or not existing nonlinear terms violate the unobservability/uncontrollability property.