Analysis and Design of Complex-Valued Linear Systems

This paper studies a class of complex-valued linear systems whose state evolution dependents on both the state vector and its conjugate. The complex-valued linear system comes from linear dynamical quantum control theory and is also encountered when a normal linear system is controlled by feedback containing both the state vector and its conjugate that can provide more design freedom. By introducing the concept of bimatrix and its properties, the considered system is transformed into an equivalent real-representation system and a non-equivalent complex-lifting system, which are normal linear systems. Some analysis and design problems including solutions, controllability, observability, stability, eigenvalue assignment, stabilization, linear quadratic regulation (LQR), and state observer design are then investigated. Criterion, conditions, and algorithms are provided in terms of the coefficient bimatrices of the original system. The developed approaches are also utilized to investigate the so-called antilinear system which is a special case of the considered complex-valued linear system. The existing results on this system have been improved and some new results are established.Comment: 19 page

Regional pole assignment with eigenstructure robustness

The paper provides a computational procedure for a type of robust regional pole assignment problem. It allows closed-loop poles to be settled at certain perturbation insensitive locations within some prespecified regions in the complex plane. The novelty of our approach lies in the versatility of the proposed algorithm which provides a rich set of constrained subregions applicable for the assignment of individual or subsets of closed-loop poles, in contrast to other conventional regional pole assignment methods. The algorithm is based on a gradient flow formulation on a differentiable potential function which provides a minimizing solution for the Frobenius condition number of the closed-loop eigenvector matrix. A numerical example is employed to illustrate the technique. The improvement on the eigenstructure robustness is compared with different kinds of constrained region.link_to_subscribed_fulltex