Stability analysis of fractional-order linear system with PID controller in the output feedback structure subject to input saturation

Controllability and observability for fractal linear dynamical systems

“…More theoretical and application problems are discussed in (Agrawal, 2007; Athans and Falb, 2013; Bryson and Ho, 2018; MacCluer, 2013; Naidu, 2002). Theory of controllability were used in studying fractional evolution equations such as (Kumar and Kumar, 2017; Kumar and Kumar, 2019), and the application of controllability was used in studying functional differential equations such as (Kumar and Kumar, 2015; Shukla and Patel (2021a)), and other works see (Amer et al, 2022; Bengochea and Ortigueira, 2017; Biswal et al, 2022; Bouazza et al, 2021; Boudjerida and Seba, 2022; Das and Samanta, 2021; Ezzahri et al, 2018; Fiuzy and Shamaghdari, 2022; Mohtavipour et al, 2019; Ibrahim and Hameed, 2021; Singh and Pandey, 2019; Zhang et al, 2022; Lu and Zuazua, 2016). Some researchers have worked on this fractal definition such as (Chen, 2006; Chen, 2006; Chen et al, 2010; Hu et al, 2020; Yang, 2021a; Yang, 2021b; Yang, 2022a et al; Yang, 2019; Yang, 2021c; Yang et al, 2022b).…”