Robust stability and stabilization of fractional-order systems with polytopic uncertainties via homogeneous polynomial parameter-dependent matrix forms

Novel admissibility and robust stabilization conditions for fractional‐order singular systems with polytopic uncertainties

“…Remark The parameters $$$ {A}_1,{A}_2,{A}_3,{A}_4,\alpha $$$ and the research problems in Example (2) are the same as those in Example 1 in Luo and Lu [41]. However, the fractional‐order derivative coefficient matrix $$$ E $$$ in Luo and Lu [41] must be nonsingular, indicating that the methods proposed in Luo and Lu [41] are special cases of the methods proposed in this paper.…”

“…In earlier studies [39,40], the robust stability and stabilization of linear FOSs are studied, and sufficient conditions are derived in terms of linear matrix inequalities (LMIs). In order to weaken the conservatism, novel robust stability conditions for FOSs with polytopic uncertainties are obtained by using the homogeneous polynomial parameter-dependent matrix forms [41] and the over parameterization technique [42]. When time delays are considered, the fractional-order Razumikhin theorem is used to derive the robust stability and stabilization conditions for FOSs with polytopic uncertainties and mixed time delays in Dinh et al [43].…”

LMI-Based Delayed Output Feedback Controller Design for a Class of Fractional-Order Neutral-Type Delay Systems Using Guaranteed Cost Control Approach

“…Ignoring uncertainties in the dynamical models, such as parameter perturbation, can significantly compromise the controller design procedure [ 35 ]. Thus, the effects of this on the system’s stability and dynamical behavior have been examined in the literature [ 36 ]. Accordingly, a robust control algorithm is needed, while guaranteeing the system’s stability and sufficient performance.…”