Stability and stabilization of positive fractional linear systems by state-feedbacks

Abstract

Abstract. Notations of the practical stability and of the asymptotic stability of positive and cone fractional 1D and 2D linear systems are introduced. Necessary and sufficient conditions for the practical stability and the asymptotic stability of positive and cone fractional 1D and 2D linear systems are established. It is shown that the checking of the practical stability and asymptotic stability of positive 2D linear systems can be reduced to testing the stability of corresponding 1D positive linear systems. Three LMI approaches are proposed for checking the stability of positive fractional linear systems. LMI approach is applied to compute gain matrices of state-feedbacks such that closed-loop systems are positive and asymptotically stable. The proposed methods are illustrated on numerical examples.

Noninvasive acoustic blood volume measurement system for the POLVAD prosthesis

“…5). In this case pressure changes caused by changes of the volume can be approximated by (2) [15,16].…”

“…6a). The electronic part realizes the positive feedback for the acoustic part [15][16][17][18]. The signal from the microphone is amplified by a preamplifier, filtered by electronic filters, conditioned by an AGC (automatic gain control circuit) (Fig.…”

Finite zeros of positive linear continuous-time systems

“…An overview of the state of the art in positive linear systems can be found in [1][2][3] and the references therein. Some new results concerning stability of positive systems with delays and of positive fractional order systems can be found in [4,5].…”

New Stability Tests Of Positive 1D And 2D Linear Systems

“…The asymptotic stability of positive 2D linear systems without and with delays has been considered in (Kaczorek 2009a and2009b). The stability and stabilization of positive fractional linear systems by state-feedbacks have been analyzed in (Kaczorek 2010). In this paper new tests for checking asymptotic stability of positive 1D continuous-time and discrete-time linear systems without and with delays and of positive 2D linear systems described by the general and the Roesser models will be proposed.…”