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In this paper, the general perturbation problem of piecewise smoothintegrable differential systems with two switching planes is considered.Firstly, when the unperturbed system has a family of periodic orbits, the firstorder Melnikov vector function is derived which can be used to study the numberof periodic orbits bifurcated from the period annuli. Then, by using theobtained Melnikov vector function, we get an upper bound of the number ofperiodic orbits of a concrete $n$-dimensional piecewise smooth differentialsystem.

Bifurcation of periodic orbits by perturbing $n$-dimensional piecewise smooth differential systems with two switching planes