Abstract
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 are proposed. Checking of the asymptotic stability of positive 2D linear systems is reduced to checking of suitable corresponding 1D positive linear systems. It is shown that the stability tests can be also applied to checking the asymptotic stability of fractional discrete-time linear systems with delays. Effectiveness of the tests is shown on numerical examples.
Highlights
A dynamical system is called positive if its trajectory starting from any nonnegative initial state remains forever in the positive orthant for all nonnegative inputs
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 are proposed
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 have been proposed
Summary
A dynamical system is called positive if its trajectory starting from any nonnegative initial state remains forever in the positive orthant for all nonnegative inputs. The Hurwitz stability of Metzler matrices has been investigated in [11] and some new tests for checking the asymptotic stability of positive 1D and 2D linear systems have been proposed in [12]. 4. In Section 5 the tests are applied to positive 2D linear systems described by the general and Roesser models and in Section 6 the fractional discrete-time linear systems with delays. —the set of n and n n 1 , m M matrices n —the with nonnegative enset of n n Metzler matrices (real matrices with nonnegative off-diagonal entries), In —the n n identity matrix
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