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The global stability of electrical circuits composed of positive linear parts and nonlinear static element with given characteristic and positive gain feedbacks is investigated. New sufficient conditions for the global stability of this class of nonlinear positive electrical circuits are established. These new stability conditions are demonstrated on simples examples of positive nonlinear electrical...
A method for decentralized stabilization of positive descriptor linear systems is proposed. Necessary and sufficient conditions for the decentralized stabilization of the positive descriptor linear systems are established. The efficiency of proposed method is demonstrated on numerical example.
The positivity and stability of a class of fractional descriptor continuous-time nonlinear systems is addressed by the use of the Weierstrass-Kronecker decomposition of the pencil of linear part of the nonlinear systems. Sufficient conditions for the positivity and stability are established. The considerations are illustrated by examples of fractional continuous-time descriptor nonlinear systems.
The conditions for positivity and stability of a class of fractional nonlinear continuous-time systems are established. It is assumed that the nonlinear vector function is continuous, satisfies the Lipschitz condition and the linear part is described by a Metzler matrix. Using an extension of the Lyapunov method sufficient conditions for the stability are derived.
The positivity and asymptotic stability of the discrete-time nonlinear systems are addressed. Necessary and sufficient conditions for the positivity of the systems and sufficient conditions for asymptotic stability of the positive systems are established. The proposed stability tests are based on Lyapunov method. The effectiveness of the tests are demonstrated on examples.
A new class of positive 2D Roesser type models is introduced. Necessary and sufficient conditions are established for the reachability of the positive 2D Roesser type model for zero boundary conditions. It is shown that the positive 2D Roesser type model having not nilpotent system matrix is unreachable for nonzero boundary conditions. The minimum energy control problem is formulated and solved for...
The minimum energy control problem for the fractional positive continuous-time linear systems is formulated and solved. Sufficient conditions for the existence of solution to the problem are established. A procedure for solving of the problem is proposed and illustrated by numerical examples.
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