Simple conditions for robust stability of positive discrete-time linear systems with delays
Robust stability of positive continuous-time linear systems with delays
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.
Minimal realization for positive multivariable linear systems with delay
The realization problem for positive multivariable discrete-time systems with one time delay is formulated and solved. Conditions for the solvability of the realization problem are established. A procedure for the computation of a minimal positive realization of a proper rational matrix is presented and illustrated by an example.
Simple conditions for practical stability of positive fractional discrete-time linear systems
In the paper the problem of practical stability of linear positive discrete-time systems of fractional order is addressed. New simple necessary and sufficient conditions for practical stability and for practical stability independent of the length of practical implementation are established. It is shown that practical stability of the system is equivalent to asymptotic stability of the corresponding standard positive discrete-time systems of the same order. The discussion is illustrated with numerical...
Computer methods for stability analysis of the Roesser type model of 2D continuous-discrete linear systems
Asymptotic stability of models of 2D continuous-discrete linear systems is considered. Computer methods for investigation of the asymptotic stability of the Roesser type model are given. The methods require computation of eigenvalue-loci of complex matrices or evaluation of complex functions. The effectiveness of the stability tests is demonstrated on numerical examples.
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