Dynamic robust stabilization of fractional-order linear systems with nonlinear uncertain parameters: an LMI approach

This paper presents a dynamic output feedback controller with determined order for the stabilization of a class of fractional-order system with nonlinear uncertain parameters with fractional order 0 < alpha < 2. Using stability theories of fractional-order systems and linear matrix inequalities (LMIs), some sufficient conditions in the LMI form are deduced to guarantee the robustness and asymptotic stabilization of the system. Designing a dynamic robust controller, along with all its useful features, leads to more unknown parameters in comparison with a static controller and makes controller design procedure more difficult due to more complex constraints that must be solved. In this paper, using proper lemmas and theorems, LMI techniques, and suitable solvers and parsers the difficulty of designing such controllers has been overcome. Simulation results of three different numerical examples illustrate that the proposed sufficient theoretical results are applicable and effective for tackling robust stabilization problems.