Stabilization of Input Derivative Positive Systems and its Utilization in Positive Singular Systems

• Published in: International Conference on Control, Decision and Information Technologies (Online) pp. 615 - 620
• Main Authors: Shafai, Bahram, Zarei, Fatemeh, Moradmand, Anahita
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.07.2024
• Subjects: Information technology; State feedback
• ISSN: 2576-3555
• DOI: 10.1109/CoDIT62066.2024.10708136

This paper introduces a subclass of positive systems involving input derivatives, which we formally define it as input derivative positive systems. Due to the presence of input derivatives, we provide an algebraic transformation to eliminate the derivative inputs to accommodate the process of stabilization by state feedback. This elimination transfers the input derivative in the output equation, which does not interfere with the design process. Stabilization of input derivative positive systems is performed through its equivalent transformed positive systems in standard form using LMI. To take advantage of this stabilization process, we utilize it for stabilization of positive singular systems. Consequently, we analyze singular systems and its equivalent transformations, which admit derivative input. Thus, algebraic transformation is employed to eliminate these derivative inputs. Finally, we establish the connection between stabilization of positive singular systems and stabilization of input derivative systems by a modified LMI. Numerical examples are included to support the theoretical result.