Robust H∞ Control for Fractional Order Systems with Order α (0 < α < 1)

Abstract

In the paper, H∞ and robust H∞ control for fractional order systems (FOS) with order 0&lt;α&lt;1 are studied. Firstly, necessary and sufficient conditions of H∞ control and state feedback controller design are proposed. Then, robust H∞ control for FOS with uncertainty is studied, and state feedback controller is designed. These conditions are based on linear matrix inequalities (LMI) and can be easily solved by the LMI toolbox. Finally, the effectiveness of these conditions is verified by two numerical examples.

Dynamic event-triggered-based anti-disturbance control for uncertain LPV systems

“…Multiplying the inequality (19) to the left and right by 𝑑𝑖𝑎𝑔{𝐼, Υ(𝜛), 𝐼} and applying the Schur complement lemma again we can obtain the inequality (18).…”

“…To obtain a minimal 𝐿 2 gain lever, the following optimization problem can be utilized in the design process: min 𝑠.𝑡. (18) 𝛼 𝑄(𝜛)>0…”

Dynamic event‐triggered‐based anti‐disturbance control for uncertain LPV systems

“…Proof. From Theorem 2, it is clear that if (18) is ensured, then the issue of dynamic event-triggered-based anti-disturbance for the system (1) is addressed.…”

“…The H ∞ control issue for many control systems have been investigated, such as the switched systems 15,16 and the frctional systems. [17][18][19] There have been many studies on the anti-disturbance control issue for LPV system over the past decades. In Refeerences 20-22, the H ∞ anti-disturbance control issue were studied for LPV system.…”

“…As a special robust control method, $$$ {H}_{\infty } $$$ control plays a beneficial role in attenuating the effects of measurable unmodeled disturbances. The $$$ {H}_{\infty } $$$ control issue for many control systems have been investigated, such as the switched systems 15,16 and the frctional systems 17‐19 . There have been many studies on the anti‐disturbance control issue for LPV system over the past decades.…”