The SPRacing F3 Flight controller was designed to give awesome flight performance and smooth flightcharacteristics. 
Small, light weight and runs Clean flight/Betaflight.

This FC would be able to run at 4Khz without a problem.

Specifications

• 36x36mm board with 30.5mm mounting holes
• Weight ~6 grams
• Acro version is without Compass and Barometer Sensors
• STM32F303 CPU, 72Mhz inc FPU
• High-Capacity Flash (Acro and Deluxe)
• MPU6050 accelerometer/gyro
• MicroUSB socket
• 2x 8pin JST-SH sockets (PPM, PWM, SERIAL RX, GPIO, ADC, 3V, 5V, GND)
• 8x 3pin though-holes for pin headers for ESC/Servo connections
• 2x 4pin though-holes for pin headers for 2x serial ports
• 1x 2pin though-holes for pin headers for battery voltage
• 1x 2pin though-holes for pin headers for buzzer
• 1x 4pin JST-SH socket for I2C
• 1x 4pin JST-SH socket for SWD debugging