Caputo-Wirtinger integral inequality and its application to stability analysis of fractional-order systems with mixed time-varying delays. (English) Zbl 07748312
Summary: Various techniques of integral inequality are widely used to establish the delay-dependent conditions for the dynamics of differential systems so that the conservatism of conditions can be reduced. In the integer-order systems, the integral term of \(\int_\tau^\omega \dot{p}^T(s) S \dot{p}(s) ds\) often appears in the derivative of Lyapunov -Krasovskii functional, and how to scale down this term to obtain less conservative condition is a key problem. Similarly, the integral term of \(\int_\tau^\omega ({}_0^C \text{D}_s^\alpha p(s))^T S_0^C \text{D}_s^\alpha p(s) ds\) with fractional derivative may also be encountered in the analysis of dynamical behaviors for fractional-order systems. In view of this, the paper intends to construct several novel fractional Wirtinger integral inequalities under the sense of Caputo derivative, and to investigate the stability of fractional-order systems with mixed time-varying delays based on the constructed Caputo-Wirtinger integral inequalities. Meanwhile, in order to analyze the stability for our concerned models by the new inequalities, two new theorems of generalized fractional-order Lyapunov direct method are given. Finally, a numerical example is designed to validate the correctness and practicability of the obtained results.
MSC:
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
| 35R11 | Fractional partial differential equations |
| 93C43 | Delay control/observation systems |
Keywords:
Caputo-Wirtinger integral inequality; fractional-order systems; mixed time-varying delays; stability; Lyapunov-Krasovskii functionalReferences:
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