This article studies the PBFT-based sharded permissioned blockchain, which executes in either a local datacenter or a rented cloud platform. In such permissioned blockchain, the transaction (TX) assignment strategy could be malicious such that the network shards may possibly receive imbalanced transactions or even bursty-TX injection attacks. An imbalanced transaction assignment brings serious threats to the stability of the sharded blockchain. A stable sharded blockchain can ensure that each shard processes the arrived transactions timely. Since the system stability is closely related to the blockchain throughput, how to maintain a stable sharded blockchain becomes a challenge. To depict the transaction processing in each network shard, we adopt the Lyapunov Optimization framework. Exploitingdrift-plus-penalty(DPP) technique, we then propose an adaptive resource-allocation algorithm, which can yield the near-optimal solution for each network shard while the shard queues can also be stably maintained. We also rigorously analyze the theoretical boundaries of both the system objective and the queue length of shards. The numerical results show that the proposed algorithm can achieve a better balance between resource consumption and queue stability than other baselines. We particularly evaluate two representative cases of bursty-TX injection attacks, i.e., the continued attacks against all network shards and the drastic attacks against a single network shard. The evaluation results show that the DPP-based algorithm can well alleviate the imbalanced TX assignment, and simultaneously maintain high throughput while consuming fewer resources than other baselines.