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This paper considers the systematic design of robust stabilizing state feedback controllers for fractional-order nonlinear systems. By using the Lyapunov direct method and a recent result on the Caputo fractional derivative of a quadratic function, stabilizability conditions expressed in terms of linear matrix inequalities are derived. The controllers can then be derived by using existing computationally effective convex algorithms. Two numerical examples with simulation results are provided to demonstrate the effectiveness of our results.

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In this paper, we investigate the problem of guaranteed cost control of uncertain fractional-order neural networks systems with time delays. By employing the Lyapunov-Razumikhin theorem, a sufficient condition for designing a state-feedback controller which makes the closed-loop system asymptotically stable and guarantees an adequate cost level of performance is derived in terms of bilinear matrix inequalities. Two numerical examples are given to show the effectiveness of the obtained results. KEYWORDS asymptotically stable, bilinear matrix inequalities, fractional-order neural networks, guaranteed cost control Optim Control Appl Meth. 2019;40:613-625.wileyonlinelibrary.com/journal/oca

In this paper, we investigate the problem of finite‐time guaranteed cost control of uncertain fractional‐order neural networks. Firstly, a new cost function is defined. Then, by using linear matrix inequalities (LMIs) approach, some new sufficient conditions for the design of a state feedback controller which makes the closed‐loop systems finite‐time stable and guarantees an adequate cost level of performance are derived. These conditions are in the form of linear matrix inequalities, which therefore can be efficiently solved by using existing convex algorithms. Finally, two numerical examples are given to illustrate the effectiveness of the proposed method.