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Robust stability of positive continuous-time linear systems with delays

Busłowicz M.

International Journal of Applied Mathematics and Computer Science

2010

Vol. 20, no 4

665-670

The paper is devoted to the problem of robust stability of positive continuous-time linear systems with delays with structured perturbations of state matrices. Simple necessary and sufficient conditions for robust stability in the general case and in the case of systems with a linear uncertainty structure in two sub-cases: (i) a unity rank uncertainty structure and (ii) nonnegative perturbation matrices are established. The problems are illustrated with numerical examples.

Simple conditions for robust stability of positive discrete-time linear systems with delays

Busłowicz M.

Control and Cybernetics

2010

Vol. 39, no 4

1159-1171

The paper is devoted to the problem of robust stability of positive linear discrete-time systems with delays in the case of structured perturbations of state matrices. Simple new necessary and sufficient conditions for robust stability in the general case and in the case of system with linear uncertainty structure are established for two sub-cases: 1) unity rank uncertainty structure, 2) non-negative perturbation matrices. It is shown that robust stability of the positive discrete-time linear system with delays is equivalent to: 1) robust stability of the corresponding positive system without delays of the same order as time-delay system - in the general case, 2) asymptotic stability of finite family of the positive vertex systems without delays - in the case of a linear unity rank uncertainty structure, 3) asymptotic stability of only one positive vertex system without delays - in the case of a linear uncertainty structure with non-negative perturbation matrices.

Robust stability of positive discrete-time linear systems with multiple delays with linear unity rank uncertainty structure or non-negative perturbation matrices

Busłowicz M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2007

Vol. 55, nr 1

1-5

Simple necessary and sufficient conditions for robust stability of the positive linear discrete-time systems wit h delays with linear uncertainty structure in two cases: 1) unity rank uncertainty structure, 2) non-negative perturbation matrices, are established. The proposed condi-tions are compared wit h the suitable conditions for the standard systems. The considerations are illustrated by numerical examples.