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.
The paper presents a linear control system framework for design of technology-based games for pedagogical rehabilitation of children with special learning needs as a central component of the proposed cyber-physical system for inclusive education. The novelty is in explicitly addressing the issue of quantitatively estimating the improvement of games in the desired direction during the design process. An advantage of the proposed approach is its applicability to small groups of children playing diverse sets of games without loss of generalisability of the linear system's model assumptions. Statistically justified experimental results are reported as providing support to the main hypotheses of the present study.
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