Algebraic criteria for global stability analysis of non-linear systems
Systems Analysis Modelling Simulation
A Kronecker product approach of stability domain determination for non-linear continuous systems
Systems Analysis Modelling Simulation
A numerical method for the stability analysis of quasi-polynomial vector fields
Nonlinear Analysis: Theory, Methods & Applications - Theory and methods
Reduced optimal control of nonlinear singularly perturbed systems
Systems Analysis Modelling Simulation
Computation of Lyapunov functions for smooth nonlinear systems using convex optimization
Automatica (Journal of IFAC)
On the design of an obstacle avoiding trajectory: Method and simulation
Mathematics and Computers in Simulation
Improved gradient-based neural networks for online solution of Lyapunov matrix equation
Information Processing Letters
Mathematics and Computers in Simulation
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In the stability study of nonlinear systems, not to found feasible solution for the LMI problem associated with a quadratic Lyapunov function shows that it doesn't exist positive definite quadratic Lyapunov function that proves stability of the system, but doesn't show that the system isn't stable. So, we must search for other Lyapunov functions. That's why, in the present paper, the construction of polynomial Lyapunov candidate functions is investigated and sufficient conditions for global asymptotic stability of analytical nonlinear systems are proposed to allow computational implementation. The main keys of this work are the description of the nonlinear studied systems by polynomial state equations, the use of an efficient mathematical tool: the Kronecker product; and the non-redundant state formulation. These notations allow algebraic manipulations and make easy the extension of the stability analysis associated to quadratic or homogeneous Laypunov functions towards more general functions. The advantage of the proposed approach is that the derived conditions proving the stability of the studied systems can be presented as linear matrix inequalities (LMIs) feasibility tests and the obtained results can show in some cases how the polynomial Lyapunov functions leads to less conservative results than those obtained via quadratic (QLFs) or monomial Laypunov functions. This contribution to the stability analysis of high order nonlinear continuous systems can be extended to the stability, robust analysis and control of other classes of systems.