Guaranteed cost control of fractional-order switched systems with mixed time-varying delays. (English) Zbl 1538.34302
Summary: This research paper investigates the problem of guaranteed cost control for a specific class of fractional-order switched systems characterized by both discrete and distributed time delays. By employing the linear matrix inequality (LMI) approach combined with the refined fractional-order Razumikhin theorem, a constructive geometric design of switching laws is developed to design a guaranteed cost controller ensuring the closed loop system not only asymptotically stable but also guarantees an adequate level of performance. The obtained conditions are dependent on the delays arising from the upper bound of the distributed time delays. These conditions are formulated in the form of linear matrix inequalities, which offers the advantage of efficient solvability using established convex algorithms. Two numerical examples with simulation results are provided to validate the efficacy of the proposed approach.
MSC:
| 34K35 | Control problems for functional-differential equations |
| 34K20 | Stability theory of functional-differential equations |
| 34K39 | Discontinuous functional-differential equations |
| 34K37 | Functional-differential equations with fractional derivatives |
Keywords:
guaranteed cost control problems; fractional-order switched systems; discrete and distributed time-varying delays; fractional-order Razumikhin method; linear matrix inequalitiesReferences:
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