Stabilization of Positive Linear Discrete-Time Systems by Using a Brauer’s Theorem

Abstract

The stabilization problem of positive linear discrete-time systems (PLDS) by linear state feedback is considered. A method based on a Brauer's theorem is proposed for solving the problem. It allows us to modify some eigenvalues of the system without changing the rest of them. The problem is studied for the single-input single-output (SISO) and for multi-input multioutput (MIMO) cases and sufficient conditions for stability and positivity of the closed-loop system are proved. The results are illustrated by numerical examples and the proposed method is used in stochastic systems.

Stabilization of discrete-time LTI positive systems

“…Applicable methods for stabilization of positive linear discrete-time systems, maintaining its positivity when using linear state feedback, are given in [10], [11], [12].…”

Fault Residuals Based on Distributed Discrete-Time Linear Kalman Filtering

“…where F is a left-stochastic matrix [25], t s ¼ 0:05 s, and the Gaussian noise covariance matrices are R ¼ 0:003 and Q ¼ 0:002 I 4 . The behavior of the system is changed by the state-feedback control Note, the steady states of F c are absorbing states.…”

Mixed H2/H∞ Control Synthesis for Discrete-time Linear Positive Systems using Enhanced Set of Linear Matrix Inequalities

“…Many structures are alternating in design, to reflect the specific structure of Metzlerian continuous-time systems [6] or positive discrete-time linear systems [3], [20], or in solving problem of diagonal stabilisation of the closed-loop system [13], [14]. Because of the positivity constraints, the synthesis of positive systems can be limited by using linear programming [1] for some problems implying from parametric constrain effects.…”