Structure-Preserving Algorithms for Periodic Discrete-Time Algebraic Riccati Equations

MPC of constrained discrete-time linear periodic systems — A framework for asynchronous control: Strong feasibility, stability and optimality via periodic invariance

“…See Chu et al (2004) and Varga (2007Varga ( , 2008 for solution methods and conditions for the existence of solutions of RP-DAREs.…”

“…This paper was recommended for publication in revised form by Associate Editor Tongwen Chen under the direction of Editor Ian R. Petersen. This work was supported in part by the Program of Promotion of Environmental Improvement to Enhance Young Researchers' Independence under the Special Coordination Funds for Promoting Science and Technology, Japan Ministry of Education, Culture, Sports, Science and Technology. periodic systems with time-dependent dimensions in Chu, Fan, Lin, and Wang (2004) and Varga (2007Varga ( , 2008. Invariant sets (Blanchini, 1999) are indispensable in constrained MPC (Mayne et al, 2000), as they yield tools to engineer the closed-loop behavior of MPC control laws with a finite prediction horizon.…”

An Overview of Recent Developments in Computational Methods for Periodic Systems

“…The solution of the PRDARE (7) for constant dimensions has been considered in (Bojanczyk et al, 1992;Hench and Laub, 1994;Benner et al, 2002), but PRDAREs with time-varying dimensions have been considered only recently in (Chu et al, 2004). A standard assumption in all these algorithms is the invertibility of R k .…”

“…Recently, general algorithms to solve PRDARE for timevarying dimensions and possibly singular R k have been developed (Varga, 2005a;Varga, 2007c). The new algorithms can be seen as extensions of both the periodic QZ decomposition based approach (Bojanczyk et al, 1992;Hench and Laub, 1994) as well as of "fast" methods (Benner et al, 2002;Chu et al, 2004).…”

Reordering the Eigenvalues of a Periodic Matrix Pair with Applications in Control

“…Collapsing the periodic matrix pair into a single matrix pair [2], [3], [11] offers a more robust alternative than forming Π, especially when some of the factors E k are nearly singular. This approach, which was shown to be numerically backward stable for p = 2, is based on the following lemma.…”