The Lyapunov stability method is the most popular and applicable stability analysis tool of nonlinear dynamic systems. However, there are some bottlenecks in the Lyapunov method, such as need for negative definiteness of the Lyapunov function derivative in the direction of the system’s solutions. In this paper, we develop a new theorem to dispense the need for negative definite-ness of Lyapunov...

The problem of observer design for nonlinear systems has got great attention in the recent literature. The nonlinear observer has been a topic of interest in control theory. In this research, a modified robust sliding-mode observer (SMO) is designed to accurately estimate the state variables of nonlinear systems in the presence of disturbances and model uncertainties. The observer has a simple ...

in this paper, an observer based fuzzy adaptive controller (fac) is designed fora class of large scale systems with non-canonical non-affine nonlinear subsystems. it isassumed that functions of the subsystems and the interactions among subsystems areunknown. by constructing a new class of state observer for each follower, the proposedconsensus control method solves the problem of unmeasured sta...

In this paper, the nonlinear dynamic system of equations, a type of nuclear ssion reactor is solved analytically and numerically. Considering that the direct solution of three-dimensional dynamical systems analysis and more in order to determine the stability and instability, in terms of algebraicsystems is dicult. Using certain situations in mathematics called Hurwitz criterion, Necessary and ...

In practical engineering, it is difficult to establish complex nonlinear dynamic equations based on theories of mechanics. Data-driven models are built using neural networks in this paper meet the needs high dimension, multi-scale and precision. We construct a two-coefficient loss function for whole data-driven modeling substructure according linear multi-step method. The forward Euler method c...

In order to increase the accuracy of evaluating seismic response of structures, it is critical to conduct dynamic analyses based upon precise nonlinear models being as consistent as possible with the real conditions of corresponding structures. The concentrated plasticity model including one elastic element and two nonlinear spring elements at both ends has been considered within the research c...

In this paper, a novel problem of observer-based adaptive fuzzy fractional control for fractional order dynamic systems with commensurate orders is investigated; the control scheme is constructed by using the backstepping and adaptive technique. Dynamic surface control method is used to avoid the problem of “explosion of complexity” which is caused by backstepping design process. Fuzzy logic sy...