13 papers
Sum of Squares Decompositions and Rank Bounds for Biquadratic Forms
Liqun Qi, Chunfeng Cui, Yi Xu
We study SOS properties of biquadratic forms. For the class of partially symmetric biquadratic forms, we establish necessary and sufficient conditions for positive semi-definitenes…
Sum of Squares Decompositions for Structured Biquadratic Forms
Yi Xu, Chunfeng Cui, Liqun Qi
This paper studies sum-of-squares (SOS) representations for structured biquadratic forms. We prove that diagonally dominated symmetric biquadratic tensors are always SOS. For the s…
The Power Method for Non-Hermitian Dual Quaternion Matrices
Hao Yang, Liqun Qi, Chunfeng Cui
This paper proposes a power method for computing the dominant eigenvalues of a non-Hermitian dual quaternion matrix (DQM). Although the algorithmic framework parallels the Hermitia…
Structured Symmetric Tensors
Liqun Qi, Chunfeng Cui, Yi Xu
In this paper, we study structured symmetric tensors. We introduce several new classes of structured symmetric tensors: completely decomposable (CD) tensors, strictly sum of square…
Completely Positive Biquadratic Tensors
Liqun Qi, Chunfeng Cui, Haibin Chen +1
In this paper, we systemically introduce completely positive biquadratic (CPB) tensors and copositive biquadratic tensors. We show that all weakly CPB tensors are sum of squares te…
A Dual Quaternion Control Law for Formation Control of Multiple 3-D Rigid Bodies
Chunfeng Cui, Liqun Qi, Hao Chen +1
This paper studies the integrated position and attitude control problem for multi-agent systems of 3D rigid bodies. While the state-of-the-art method in [Olfati-Saber and Murray, 2…