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The stability of time-invariant positive nonlinear systems is addressed. Necessary conditions for the stability of positive time-invariant continuous-time and discrete-time nonlinear systems are established. It is shown that the positive nonlinear systems are asymptotically stable only if the corresponding positive linear systems are asymptotically stable. Considerations are illustrated by numerical...
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.
The asymptotic stability of positive continuous-time linear systems with delays is addressed. It is shown that: 1) the asymptotic stability of the positive systems with delays is independent of their delays, 2) the checking of the asymptotic stability of the positive systems with delays can be reduced to checking of the asymptotic stability of positive systems without delays. Simple stability conditions...
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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