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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 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 classical Cayley-Hamilton theorem is extended to Drazin inverse matrices. A new procedure based on this extension for computation of the Drazin inverse matrices is proposed.
The classical Cayley-Hamilton theorem is extended to the fractional descriptor continuous-time linear systems. First the theorem is extended to fractional descriptor linear systems with commuting matrices and next to any pair of matrices of the descriptor linear systems. The extensions are based on the application of the Lagrange-Sylvester formula of the function of matrices.
The problem of existence of reachable pairs (A, B) of discrete-time linear systems is formulated and solved. Necessary and sufficient conditions for the reachability of standard and positive full order and fractional order discrete-time linear systems are recalled. The existence of the reachable pairs (A, B) of the systems is investigated. Considerations are illustrated by numerical examples.
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 positivity and asymptotic stability of the discrete-time and continuous-time nonlinear systems are addressed. Sufficient conditions for the positivity and asymptotic stability of the nonlinear systems are established. The proposed stability tests are based on an extension of the Lyapunov method to the positive 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 notion of locally positive nonlinear time-varying linear systems is introduced. Necessary and sufficient conditions for the local positivity of nonlinear time-varying systems are established. The concept of local reachability in the direction of a cone is introduced and sufficient conditions for the local reachability in the direction of a cone of this class of nonlinear systems are presented.
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...
A new notion of a 2D (P,Q,V)-cone system is introduced. Necessary and sufficient conditions for the existence of a realization of a given proper transfer matrix are established. A procedure is proposed for computation of a realization of a given transfer matrix of the 2D (P,Q,V)-cone system. It is shown that there exists a realization of the transfer matrix T(z1,z2) of a 2D (P,Q,V)-cone system if...
A notion of positive fractional discrete-time system is introduced. Necessary and sufficient conditions are established for the positivity, reachability and controllability to zero of fractional discrete-time linear systems. The classical Cayley-Hamilton theorem is extended for the positive fractional systems.
Necessary and sufficient conditions for the positivity and reachability of electrical circuits composed of resistors, coils and capacitors are given. The minimum energy control problem for the positive electrical circuits is formulated and solved. Procedure for computation of the optimal input and minimal value of the performance index is proposed and illustrated by a numerical examples.
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.
The problem of positive asymptotically stable realizations and relations between them is addressed. Sufficient conditions for existence of the positive asymptotically stable realizations of linear continuous-time systems with real negative poles and zeros are established. A matrix of similarity transformation is proposed which preserves the positivity and asymptotic stability of the linear systems.
Conditions for the existence of positive stable realizations with system Metzler matrices for linear continuous-time systems are established. A procedure for finding a positive stable realization with system Metzler matrix based on similarity transformation of proper transfer matrices is proposed and demonstrated on numerical examples. It is shown that if the poles of stable transfer matrix are real...
Conditions for the existence of positive stable realizations with system Metzler matrices for proper transfer function are established. A method based on the decomposition of transfer functions into the first, second and third orders transfer functions for computation of positive stable realizations is proposed. A method for computation of positive stable realizations of transfer functions with real...
Necessary and sufficient conditions are established for the positivity of bilinear discrete-time systems with delays. The controllability to zero of the bilinear positive systems with delays is addressed. Necessary and sufficient conditions for the controllability to zero of positive bilinear systems with delays are formulated and proved. The considerations are illustrated by examples.
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