```ts
export function mergeIntervals(intervals: number[][]): number[][] {
  if (!intervals.length) return [];

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

  const merged: number[][] = [];
  let currentInterval = intervals[0];

  for (const nextInterval of intervals.slice(1)) {
    if (currentInterval[1] < nextInterval[0]) {
      merged.push(currentInterval);
      currentInterval = nextInterval;
    } else if (currentInterval[1] < nextInterval[1]) {
      currentInterval[1] = nextInterval[1];
    }
  }

  merged.push(currentInterval);

  for (const [start, end] of merged) {
    if (start > end) {
      throw new Error("Invalid interval: start must be less than or equal to end");
    }
  }

  return merged;
}
```