This work considers the problem of observer design for rectangular descriptor systems with nonlinearities satisfying incremental quadratic constraints. The observer design is feasible under the satisfaction of a linear matrix inequality and some algebraic relations in the system matrices. The special case of nonlinearities in the output is also considered. Finally, the developed approach is applied to the problem of secure communications and illustrated through numerical examples.

In this article, a fuel tank is coupled with gyrostat in a moving spacecraft to discuss its dynamical behaviour and bringing stability in velocity vectors. Parametric study is performed using Hopf bifurcation to find the bifurcation parameter for a considered mechanical model. Furthermore, a region is constructed in which negligible limit cycles appear around unstable spirals for angular momentum greater than bifurcation point. Based on local dynamical analysis, trajectories of angular velocities are observed with respect to damping constant, which is formulated in the form of bifurcation parameter. Moreover, a controller is designed in this article for considered dynamical system by achieving global stability, with the help of Lyapunov theory, into the spacecraft coupled with filled fuel tank, and their results are compared with effective spacecraft control strategies to observe the effectiveness of our proposed control technique. Finally, in presented research, numerical simulations are performed using MATLAB for validation of analytical results, which the authors have achieved for Hopf bifurcation and designed controller.

We derive new mean value theorems for functionals associated with Hadamard inequality for convex functions on the coordinates. We present some Hadamard type inequalities and related results for m-convex functions on the coordinates.

In this paper, we used Lyapunov theory and Linear Matrix Inequalities (LMI) to design a generalized observer by adding more complexity in the output of the dynamic systems. Our designed observer is based on the optimization problem, minimizing error between trajectories of master and slave systems subject to the incremental quadratic constraint. Moreover, an algorithm is given in our paper used to demonstrate a method for obtaining desired observer and gain matrixes, whereas these gain matrixes are obtained with the aid of LMI and incremental multiplier matrix (IMM). Finally, discussion of two examples are an integral part of our study for the explanation of achieved analytical results using MATLAB and SCILAB.

In this work, a novel hyperjerk system, with hyperbolic sine function as the only nonlinear term, is proposed, as a modification of a hyperjerk system proposed by Leutcho et al. First, a dynamical analysis on the system is performed and interesting phenomena concerning chaos theory, such as route to chaos, antimonotonicity, crisis, and coexisting attractors, are studied. For this reason, the system’s bifurcation diagrams with respect to different parameter values are plotted and its Lyapunov exponents are computed. Afterwards, the synchronization of the system is considered, using active control. The proposed system is then applied, as a chaotic generator, to the problem of chaotic path planning, using a combination of sampling and a modulo tactic technique.