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An extension of the Cayley-Hamilton theorem for nonlinear time-varying systems

100%

Kaczorek T.

International Journal of Applied Mathematics and Computer Science

2006

tom 16

nr 1

141-145

The classical Cayley-Hamilton theorem is extended to nonlinear time-varying systems with square and rectangular system matrices. It is shown that in both cases system matrices satisfy many equations with coefficients being the coefficients of characteristic polynomials of suitable square matrices. The proposed theorems are illustrated with numerical examples.

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Positivity and linearization of a class of nonlinear continuous-time systems by state feedbacks

88%

Kaczorek T.

International Journal of Applied Mathematics and Computer Science

2015

tom 25

nr 4

827-831

The positivity and linearization of a class of nonlinear continuous-time system by nonlinear state feedbacks are addressed. Necessary and sufficient conditions for the positivity of the class of nonlinear systems are established. A method for linearization of nonlinear systems by nonlinear state feedbacks is presented. It is shown that by a suitable choice of the state feedback it is possible to obtain an asymptotically stable and controllable linear system, and if the closed-loop system is positive then it is unstable.

Ograniczanie wyników

2 International Journal of Applied Mathematics and Computer Science

2 Kaczorek T.

1 2015

1 2006

Wyniki wyszukiwania

An extension of the Cayley-Hamilton theorem for nonlinear time-varying systems

Positivity and linearization of a class of nonlinear continuous-time systems by state feedbacks