Cole J W, Calico R A. Nonlinear oscillations of a controlled periodic system. AIAA Journal of Guidance, Control, and Dynamics, 1992, 15(3): 627-633
[2]
Allen M S, Sracic M W, Chauhan S, Hansen M H. Output-only modal analysis of linear time-periodic systems with application to wind turbine simulation data. Mechanical Systems and Signal Processing, 2011, 25(4): 1174-1191
[3]
Vaidyanathan P P. Multirate digital filters, filter banks, polyphase networks, and applications: a tutorial. Proceedings of the IEEE, 1990, 78(1): 56-93
[4]
Kranc G M. Input-output analysis of multirate feedback systems. IRE Transactions on Automatic Control, 1957, 3(1): 21-28
[5]
Jury E I, Mullin F J. The analysis of sampled-data control systems with a periodically time-varying sampling rate. IRE Transactions on Automatic Control, 1959, AC-4(1): 15-21
[6]
Meyer R A, Burrus C S. A unified analysis of multirate and periodically time-varying digital filters. IEEE Transactions on Circuits and Systems, 1975, 22(3): 162-168
[7]
Flamm D S. A new shift-invariant representation for periodic linear systems. Systems and Control Letters, 1991, 17(1): 9-14
[8]
Colaneri P, Kucera V. The model matching problem for periodic discrete-time systems. IEEE Transactions on Automatic Control, 1997, 42(10): 1472-1476
[9]
Bittanti S, Guardabassi G, Maffezzoni C, Silverman L. Periodic systems: controllability and the matrix Riccati equation. SIAM Journal on Control and Optimization, 1978, 16(1): 37-40
[10]
Colaneri P, Souza C D, Kucera V. Output stabilizability of periodic systems: necessary and sufficient conditions. In: Proceedings of the 1998 American Control Conference. Philadelphia, USA: IEEE, 1998. 2795-2796
[11]
Desoer C A, Schulman J O. Zeros and poles of matrix transfer functions and their dynamical interpretation. IEEE Transactions on Circuits and Systems, 1974, 21(1): 3-8
[12]
Macfarlane A G J, Karcanias N. Poles and zeros of linear multivariable systems: a survey of the algebraic, geometric and complex-variable theory. International Journal of Control, 1976, 24(1): 33-74
[13]
Bolzern P, Colaneri P, Scattolini R. Zeros of discrete-time linear periodic systems. IEEE Transactions on Automatic Control, 1986, 31(11): 1057-1058
[14]
Grasselli O M, Longhi S. Finite zero structure of linear periodic discrete-time systems. International Journal of Systems Science, 1991, 22(10): 1785-1806
[15]
Colaneri P, Longhi S. The realization problem for linear periodic systems. Automatica, 1995, 31(5): 775-779
[16]
Gohberg I, Kaashoek M A, Lerer L. Minimality and realization of discrete time-varying systems. Operator Theory: Advances and Applications, 1992, 56: 261-296
[17]
Varga A. Computation of minimal periodic realizations of transfer-function matrices. IEEE Transactions on Automatic Control, 2004, 49(1): 146-149
[18]
Farhood M, Beck C L, Dullerud G E. Model reduction of periodic systems: a lifting approach. Automatica, 2005, 41(6): 1085-1090
[19]
Kwon W H, Pearson A E. On the stabilization of a discrete constant linear system. IEEE Transactions on Automatic Control, 1975, 20(6): 800-801
[20]
de Nicolao G, Strada S. On the stability of receding-horizon LQ control with zero-state terminal constraint. IEEE Transactions on Automatic Control, 1997, 42(2): 257-260
[21]
de Nicolao G. Cyclomonotonicity and stabilizability properties of solutions of the difference periodic Riccati equation. IEEE Transactions on Automatic Control, 1992, 37(9): 1405-1410
[22]
Bittanti S, Colaneri P, Nicolao G D. The difference periodic Riccati equation for the periodic prediction problem. IEEE Transactions on Automatic Control, 1988, 33(8): 706-712
[23]
Zhou B, Duan G R, Lin Z L. A parametric periodic Lyapunov equation with application in semi-global stabilization of discrete-time periodic systems subject to actuator saturation. Automatica, 2011, 47(2): 316-325
[24]
Sun K, Xie G M. Analysis and control of a class of uncertain linear periodic discrete-time systems. Applied Mathematics and Mechanics, 2009, 30(4): 475-488
[25]
Longhi S, Zulli R. A robust periodic pole assignment algorithm. IEEE Transactions on Automatic Control, 1995, 40(5): 890-894
[26]
Aeyels D, Willems J L. Pole assignment for linear periodic systems by memoryless output feedback. IEEE Transactions on Automatic Control, 1995, 40(4): 735-739
[27]
Lv L L, Duan G R, Su H B. Robust dynamical compensator design for discrete-time linear periodic systems. Journal of Global Optimization, 2012, 52(2): 291-304
[28]
Sreedhar J, van Dooren P, Bamieh B. Computing H∞-norm of discrete-time periodic systems-a quadratically convergent algorithm. In: Proceedings of the 1997 European Control Conference. Brussels, Belgium, 1997
[29]
Peaucelle D, Ebihara Y, Arzelier D. Robust H2 perfomance of discrete-time periodic systems: LMIs with reduced dimensions. In: Proceedings of the 17th World Congress the International Federation of Automatic Control. Seoul, Korea: IFAC, 2008. 1348-1353
[30]
Fadali M S, Gummuluri S. Robust observer-based fault detection for periodic systems. In: Proceedings of the 2001 American Control Conference. Arlington, VA: IEEE, 2001. 464-469
[31]
Zhang P, Ding S X, Wang G Z, Zhou D H. Fault detection of linear discrete-time periodic systems. IEEE Transactions on Automatic Control, 2005, 50(2): 239-244
[32]
Djemili I, Aitouche A, Bouamama B O. Sensors FDI scheme of linear discrete-time periodic systems using principal component analysis. In: Proceedings of 2010 Conference on Control and Fault-Tolerant Systems. Nice, France: IEEE, 2010. 203-208
[33]
van Paul D, Sreedhar J. When is a periodic discrete-time system equivalent to a time-invariant one? Linear Algebra and its Applications, 1994, 212-213: 131-151
[34]
DaCunha J J, Davis J M. A unified Floquet theory for discrete, continuous, and hybrid periodic linear systems. Journal of Differential Equations, 2011, 251(11): 2987-3027% (吕灵灵, 段广仁, 周彬. 线性离散周期系统输出反馈参数化极点配置. 自动化学报, 2010, 36(1): 113-120)%
[35]
Sreedhar J, van Dooren P. Periodic Schur form and some matrix equations. Systems and Networks: Mathematical Theory and Applications, 1993, 77: 339-362%
[36]
Zheng Yu-Hong, Wang Ping. A new approach to control satellite attitude via magnetorquers. Journal of Astronautics, 2000, 21(3): 94-99 (郑育红, 王平. 一种用磁力矩器控制卫星姿态的新方法. 宇航学报, 2000, 21(3): 94-99)
[37]
Nie J B, Sheh E, Horowitz R. Optimal H∞ control for hard disk drives with an irregular sampling rate. In: Proceedings of 2011 American Control Conference. San Francisco, USA: IEEE, 2011. 5382-5387
[38]
Chauvin J, Corde G, Petit N, Rouchon P. Periodic input estimation for linear periodic systems: automotive engine applications. Automatica, 2007, 43(6): 971-980
[39]
Wornell G W. Emerging applications of multirate signal processing and wavelets in digital communications. Proceedings of the IEEE, 1996, 84(4): 586-603
[40]
Bittanti S, Colaneri P. Invariant representations of discrete-time periodic systems. Automatica, 2000, 36(12): 1777-1793
[41]
Rriedland B. Sampled-data control systems containing periodically varying members. In: Proceedings of the 1st IFAC Congress. Moscow, U.S.S.R., 1960. 361-368
[42]
Park B, Verriest E I. Canonical forms on discrete linear periodically time-varying systems and a control application. In: Proceedings of the 28th IEEE Conference on Decision and Control. Tampa, USA: IEEE, 1989. 1220-1225
[43]
Bittanti S, Bolzern P. On the structure theory of discrete-time linear systems. International Journal of Systems Science, 1986, 17(1): 33-47
[44]
Bittanti S, Colaneri P, de Nicolao G. Discrete-time linear periodic systems: a note on the reachability and controllability interval length. Systems & Control Letters, 1986, 8(1): 75-78
[45]
Bittanti S, Colaneri P. Analysis of discrete-time linear periodic systems. Control and Dynamic Systems, 1996, 78: 313-339
[46]
Bittanti S, Colaneri P. Discrete-time linear periodic systems: gramian and modal criteria for reachability and controllability. International Journal of Control, 1985, 41(4): 909-928
[47]
Bittanti S, Bolzern P, Colaneri P. The extended periodic Lyapunov lemma. Automatica, 1985, 21(5): 603-605
[48]
Francis B A, Wonham W M. The role of transmission zeros in linear multivariable regulators. International Journal of Control, 1975, 22(5): 657-681
[49]
Morse A S. Structural invariants of linear multivariable systems. SIAM Journal on Control, 1973, 11(3): 446-465
[50]
Grasselli O M, Longhi S. Zeros and poles of linear periodic multivariable discrete-time systems. Circuits, Systems and Signal Processing, 1988, 7(3): 361-380
[51]
Varga A, van Dooren P. On computing the zeros of periodic systems. In: Proceeding of the 41st IEEE Conference on Decision and Control. Las Vegas, USA: IEEE, 2002. 2546-2551
[52]
Varga A. Balancing related methods for minimal realization of periodic systems. Systems & Control Letters, 1999, 36(5): 339-349
[53]
Varga A. Balanced truncation model reduction of periodic systems. In: Proceedings of the 39th IEEE Conference on Decision and Control. Sydney, NSW: IEEE, 2000. 2379-2384
[54]
Kleinman D L. Stabilizing a discrete, constant, linear system with application to iterative methods for solving the Riccati equation. IEEE Transactions on Automatic Control, 1974, 19(3): 252-254
[55]
Kwon W H, Pearson A E. A modified quadratic cost problem and feedback stabilization of a linear system. IEEE Transactions on Automatic Control, 1977, 22(5): 838-842
[56]
de Nicolao G, Strada S. On the use of reachability Gramians for the stabilization of linear periodic systems. Automatica, 1997, 33(4): 729-732
[57]
Varga A, Pieters S. Gradient-based approach to solve optimal periodic output feedback control problems. Automatica, 1998, 34(4): 477-481
[58]
de Souza C E, Trofino A. An LMI approach to stabilization of linear discrete-time periodic systems. International Journal of Control, 2000, 73(8): 696-703
[59]
Zhou B, Zheng W X, Duan G R. Stability and stabilization of discrete-time periodic linear systems with actuator saturation. Automatica, 2011, 47(8): 1813-1820
[60]
Longhi S, Zulli R. A note on robust pole assignment for periodic systems. IEEE Transactions on Automatic Control, 1996, 41(10): 1493-1497
[61]
Sreedhar J, van Dooren P. Pole placement via the periodic Schur decomposition. In: Proceedings of the American Control Conference. San Francisco, USA: IEEE, 1993. 1563-1567
[62]
Hernández V, Urbano A M. Pole-placement problem for discrete-time linear periodic systems. International Journal of Control, 1989, 50(1): 361-371
[63]
Varga A. Robust and minimum norm pole assignment with periodic state feedback. IEEE Transactions on Automatic Control, 2000, 45(5): 1017-1022
[64]
Lv L L, Duan G R, Zhou B. Parametric pole assignment and robust pole assignment for discrete-time linear periodic systems. SIAM Journal on Control and Optimization, 2010, 48(6): 3975-3996
[65]
Varga A. Computation of L∞ norm of linear discrete-time periodic systems. In: Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems. Kyoto, Japan, 2006
[66]
Wisniewski R, Stoustrup J. Generalized H2 control synthesis for periodic systems. In: Proceedings of the American Control Conference. Arlington, VA: IEEE, 2001. 2600-2605
[67]
Farges C, Peaucelle D, Arzelier D, Daafouz J. Robust H2 performance analysis and synthesis of linear polytopic discrete-time periodic systems via LMIs. Systems & Control Letters, 2007, 56(2): 159-166
[68]
Ebihara Y, Peacelle D, Arzelier D. Periodically time-varying dynamical controller synthesis for polytopic-type uncertain discrete-time linear systems. In: Proceedings of the 47th IEEE Conference on Decision and Control. Cancun: IEEE, 2008. 5438-5443
[69]
Varga A. Design of fault detection filters for periodic systems. In: Proceedings of the 43rd IEEE Conference on Decision and Control. Paradise Island, Bahamas: IEEE, 2004. 4800-4805
[70]
Zhang P, Ding S X. Disturbance decoupling in fault detection of linear periodic systems. Automatica, 2007, 43(8): 1410-1417
[71]
Gondhalekar R, Colin N J. MPC of constrained discrete-time linear periodic systems-A framework for asynchronous control: strong feasibility, stability and optimality via periodic invariance. Automatica, 2011, 47(2): 326-333
[72]
Hayakawa Y, Jimbo T. Floquet transformations for discrete-time systems: equivalence between periodic systems and time-invariant ones. In: Proceedings of the 47th IEEE Conference on Decision and Control. Cancun, Mexico: IEEE, 2008. 5140-5145
[73]
Zhang W. Reinforcement Learning for Job-Shop Scheduling [Ph.D. dissertation], Peking University, China, 1996%
[74]
Larin V B. Solution of the discrete-time periodic Riccati equations (LMI approach). Stability and Control: Theory and Application, 2004, 6(2): 102-108
