Abstract
The global stability of positive discrete-time time-varying nonlinear systems with time-varying scalar feedbacks is investigated. Sufficient conditions for the asymptotic stability of discrete-time positive time-varying linear systems are given. The new conditions are applied to discrete-time positive time-varying nonlinear systems with time-varying feedbacks. Sufficient conditions are established for the global stability of the discrete-time positive time-varying nonlinear systems with feedbacks.
Highlights
In positive systems inputs, state variables and outputs take only nonnegative values for any nonnegative inputs and nonnegative initial conditions [1, 4, 7]
The positive discrete-time nonlinear system shown in Fig. 1 is globally stable if the matrix (16b) satisfies Theorem 5
For example applying Theorems 6 and 4 to the positive nonlinear system we may find the minimal value of k satisfying the condition (12) for which the positive time-varying nonlinear system is globally stable
Summary
State variables and outputs take only nonnegative values for any nonnegative inputs and nonnegative initial conditions [1, 4, 7]. The stability of nonlinear continuous-time standard and fractional positive systems have been analyzed in [2, 3, 5, 6, 9, 11, 12, 14, 16, 18]. The global stability of positive time-varying nonlinear feedback timevarying systems has been considered in [13]. In this paper the results of [13] will be extended to positive discrete-time timevarying nonlinear systems. - the set of n m real matrices with nonnegative entries and n n 1 , M n - the set of n n Metzler matrices (real matrices with nonnegative off-diagonal entries), In the n n identity matrix.
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