```ts
function mergeIntervals(intervals: number[][]): number[][] {
  if (intervals.some(interval => interval[0] > interval[1])) {
    throw new Error("An interval must have a start less than or equal to its end.");
  }

  intervals.sort((a, b) => a[0] - b[0]);

  let merged: number[][] = [];
  for (const interval of intervals) {
    if (merged.length === 0 || interval[0] > merged[merged.length - 1][1]) {
      merged.push(interval);
    } else {
      merged[merged.length - 1][1] = Math.max(merged[merged.length - 1][1], interval[1]);
    }
  }

  return merged;
}
```