Energy absorption capacity; a new concept for stability analysis of nonlinear dynamic systems

Abstract

Stability is the main concern considered for every system. Generally the well-known Lyapunov and input-output stability methods are utilized for the stability analysis of nonlinear systems. These methods face serious difficulties as the size and complexity of the systems increases. In this paper a new approach is presented to overcome this problem by introducing a new concept "Energy Absorption Capacity" (EAC) for every component. The EAC of the system can be derived from its component EACs considering their interaction. It is shown that the stability of every individual component is assured if its EAC has a positive value. The proposed approach is less conservative compared to a Lyapunov-based approach. This is due to its reliance on EAC as the extreme value of energy function rather than the function itself. Some examples are given to support the proposed approach.

Optimal control of large-scale singular linear systems via hierarchical strategy

“…The methodologies of large-scale systems provide such techniques through the manipulation of the system structure in some way. Hence, there has been considerable interest in the research area of modeling, analysis, and control of large-scale systems (Jamshidi, 1996; Jamshidi and Afshar, 2009; Labibi et al, 2003; Shafieirad et al, 2013; Zamani and Sadati, 2009) and many approaches are developed to investigate some important problems of large-scale systems such as adaptive fuzzy control (Li et al, 2017; Tong et al, 2017), identification and optimal control (Nguyen and Mukhopadhyay, 2016), cloud computing (Zhang et al, 2016), model reduction (Haider et al, 2017), robust variable structure observer (Mohamed et al, 2016), fuzzy modeling analysis (Zamani and Sadati, 2009; Zamani and Zarif, 2007; Zamani et al, 2011), and optimization of large-scale systems (Sadati, 2005; Sadati and Ramezani, 2009, 2010; Zhang et al, 2005).…”