New Results on H∞ Control for Nonlinear Conformable Fractional Order Systems

Non‐fragile H∞ observer for Lipschitz conformable fractional‐order systems

“…Definition [ 23 ] In order to say that s ystem (5) is exponentially stable under an H ∞ performance γ , it should be: exponentially stable whenever ω = 0 and satisfies under the zero initial condition, for ω ≠ 0. …”

“…Definition 2.5. [23 ] In order to say that system (5) is exponentially stable under an H ∞ performance γ, it should be:…”

On the Barbalat lemma extension for the generalized conformable fractional integrals: Application to adaptive observer design

“…Some recent work is examined in Abdeljawad [16] to enhance such a derivative. There has been a lot of research and description done on it, and we recommend the following references to the readers [17][18][19][20][21][22]. After that, a new extension for the conformable fractional derivative is described; see previous studies [23][24][25].…”

“…In the few last years, in Khalil et al [15], a new fractional‐order derivative has been defined named “the conformable fractional derivative.” Some recent work is examined in Abdeljawad [16] to enhance such a derivative. There has been a lot of research and description done on it, and we recommend the following references to the readers [17–22]. After that, a new extension for the conformable fractional derivative is described; see previous studies [23–25].…”

On characterisations of the input to state stability properties for conformable fractional order bilinear systems

“…[27], a framework in terms of behavioral system theory has been presented to develop a general modelling specification as well as stability conditions for conformable linear systems with a fractional differential order, and the sufficient conditions and tests for stability were provided based on linear matrix inequalities. Furthermore, several well‐behaved modelling and control methods have been newly developed under conformable derivative including conformable fractional‐order neural sliding‐mode control [34], conformable fractional optimal control [22], robust $$\mathcal {H}_{\infty }$$ control scheme for nonlinear conformable fractional‐order systems [26, 28] and conformable fractional modeling and control of complex biological system [4, 15], to mention a few.…”