A compressor, comprising: a low-pressure stage cylinder, a first high-pressure stage cylinder, a second high-pressure stage cylinder and a lower flange, wherein, the low-pressure stage cylinder, the first high-pressure stage cylinder and the second high-pressure stage cylinder are stacked, and a partition is arranged between each two adjacent cylinders, the first high-pressure stage cylinder and the second high-pressure stage cylinder are both situated at a same side of the low-pressure stage cylinder or the first high-pressure stage cylinder and the second high-pressure stage cylinder are respectively situated at two sides of the low-pressure stage cylinder, the lower flange is situated below the low-pressure stage cylinder, the first high-pressure stage cylinder and the second high-pressure stage cylinder; the first high-pressure stage cylinder has a first sliding sheet slot, and a first sliding sheet is provided in the first sliding sheet slot, the second high-pressure stage cylinder has a second sliding sheet slot, and a second sliding sheet is provided in the second sliding sheet slot, the low-pressure stage cylinder has a third sliding sheet slot, and a third sliding sheet is provided in the third sliding sheet slot; and the first high-pressure stage cylinder and the second high-pressure stage cylinder are arranged in parallel, and the first high-pressure stage cylinder and the second high-pressure stage cylinder arranged in parallel are connected to the low-pressure stage cylinder in series, the first high-pressure stage cylinder and/or the second high-pressure stage cylinder is a variable capacity cylinder, and the low-pressure stage cylinder functions as a first-stage compression cylinder; and characterized in that, two of the partitions are respectively a first partition and a second partition, and the first partition and/or the second partition is provided with a sliding-sheet control device configured to control a movement of a respective sliding sheet; or, the first partition and/or the lower flange is provided with the sliding-sheet control device; or, the second partition and/or the lower flange is provided with the sliding-sheet control device; and each of the sliding-sheet control devices corresponds to one of the sliding sheets. a low-pressure stage cylinder, a first high-pressure stage cylinder, a second high-pressure stage cylinder and a lower flange, wherein, the low-pressure stage cylinder, the first high-pressure stage cylinder and the second high-pressure stage cylinder are stacked, and a partition is arranged between each two adjacent cylinders, the first high-pressure stage cylinder and the second high-pressure stage cylinder are both situated at a same side of the low-pressure stage cylinder or the first high-pressure stage cylinder and the second high-pressure stage cylinder are respectively situated at two sides of the low-pressure stage cylinder, the lower flange is situated below the low-pressure stage cylinder, the first high-pressure stage cylinder and the second high-pressure stage cylinder; the first high-pressure stage cylinder has a first sliding sheet slot, and a first sliding sheet is provided in the first sliding sheet slot, the second high-pressure stage cylinder has a second sliding sheet slot, and a second sliding sheet is provided in the second sliding sheet slot, the low-pressure stage cylinder has a third sliding sheet slot, and a third sliding sheet is provided in the third sliding sheet slot; and the first high-pressure stage cylinder and the second high-pressure stage cylinder are arranged in parallel, and the first high-pressure stage cylinder and the second high-pressure stage cylinder arranged in parallel are connected to the low-pressure stage cylinder in series, the first high-pressure stage cylinder and/or the second high-pressure stage cylinder is a variable capacity cylinder, and the low-pressure stage cylinder functions as a first-stage compression cylinder; and