scholarly journals Discrete-Time System Conditional Optimization in the Parameter Space with Nonzero Initial Conditions

2022 ◽  
Vol 29 (1) ◽  
2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Luciano Fanti ◽  
Luca Gori ◽  
Cristiana Mammana ◽  
Elisabetta Michetti

This paper tackles the issue of local and global analyses of a duopoly game with price competition and market share delegation. The dynamics of the economy is characterised by a differentiable two-dimensional discrete time system. The paper stresses the importance of complementarity between products as a source of synchronisation in the long term, in contrast to the case of their substitutability. This means that when products are complements, players may coordinate their behaviour even if initial conditions are different. In addition, there exist multiple attractors so that even starting with similar conditions may end up generating very different dynamic patterns.


1988 ◽  
Author(s):  
Ioannis S. Apostolakis ◽  
John Diamessis ◽  
David Jordan

Author(s):  
Noriyuki Hori ◽  
Peter N. Nikiforuk ◽  
Kimio Kanai

2021 ◽  
pp. 107754632110016
Author(s):  
Liang Huang ◽  
Cheng Chen ◽  
Shenjiang Huang ◽  
Jingfeng Wang

Stability presents a critical issue for real-time hybrid simulation. Actuator delay might destabilize the real-time test without proper compensation. Previous research often assumed real-time hybrid simulation as a continuous-time system; however, it is more appropriately treated as a discrete-time system because of application of digital devices and integration algorithms. By using the Lyapunov–Krasovskii theory, this study explores the convoluted effect of integration algorithms and actuator delay on the stability of real-time hybrid simulation. Both theoretical and numerical analysis results demonstrate that (1) the direct integration algorithm is preferably used for real-time hybrid simulation because of its computational efficiency; (2) the stability analysis of real-time hybrid simulation highly depends on actuator delay models, and the actuator model that accounts for time-varying characteristic will lead to more conservative stability; and (3) the integration step is constrained by the algorithm and structural frequencies. Moreover, when the step is small, the stability of the discrete-time system will approach that of the corresponding continuous-time system. The study establishes a bridge between continuous- and discrete-time systems for stability analysis of real-time hybrid simulation.


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