
Previous Article
Minimization of the base transit time in semiconductor devices using optimal control
 PROC Home
 This Issue

Next Article
Parabolic systems with non continuous coefficients
On the central stability zone for linear discretetime Hamiltonian systems
1.  Department of Automatic Control, University of Craiova, A.I. Cuza Str. No. 13, RO1100 Craiova, Romania 
$_y_(k+1)  _y(_k) = \lambda B(__k)_y(_k) + \lambda D_(k^z_(k+1))$
$_z_(k+1)  _z(_k) = \lambda A(__k)_y(_k)  \lambda B*_(k^z_(k+1))$
where $A_k$ and $D_k$ are Hermitian matrices, $A_k$, $B_k$, $D_k$ define $N$periodic sequences, and $\lambda$ is a complex parameter. For this system a Kreintype theory of the $\lambda$zones of strong (robust) stability may be constructed. Within this theory the side $\lambda$zones’ width may be estimated using the multipliers’ “traffic rules” of Krein while the central stability zone (centered around $\lambda$ = 0) is estimated using the eigenvalues of a certain boundary value problem which is selfadjoint. In the discretetime there occur some specific differences with respect to the continuous time case due to the fact that the transition matrix (hence the monodromy matrix also) is not entire with respect to $\lambda$ but rational. During the paper we consider some specific cases (the matrix analogue of the discretized Hill equation, the Junitary and symplectic systems, real scalar systems) for which the results on the eigenvalues are complete and obtain some simplified estimates of the central stability zones.
[1] 
Xiang Xie, Honglei Xu, Xinming Cheng, Yilun Yu. Improved results on exponential stability of discretetime switched delay systems. Discrete & Continuous Dynamical Systems  B, 2017, 22 (1) : 199208. doi: 10.3934/dcdsb.2017010 
[2] 
Huan Su, Pengfei Wang, Xiaohua Ding. Stability analysis for discretetime coupled systems with multidiffusion by graphtheoretic approach and its application. Discrete & Continuous Dynamical Systems  B, 2016, 21 (1) : 253269. doi: 10.3934/dcdsb.2016.21.253 
[3] 
Sofian De Clercq, Koen De Turck, Bart Steyaert, Herwig Bruneel. Framebound priority scheduling in discretetime queueing systems. Journal of Industrial & Management Optimization, 2011, 7 (3) : 767788. doi: 10.3934/jimo.2011.7.767 
[4] 
Karl P. Hadeler. Quiescent phases and stability in discrete time dynamical systems. Discrete & Continuous Dynamical Systems  B, 2015, 20 (1) : 129152. doi: 10.3934/dcdsb.2015.20.129 
[5] 
Chuandong Li, Fali Ma, Tingwen Huang. 2D analysis based iterative learning control for linear discretetime systems with time delay. Journal of Industrial & Management Optimization, 2011, 7 (1) : 175181. doi: 10.3934/jimo.2011.7.175 
[6] 
Ran Dong, Xuerong Mao. Asymptotic stabilization of continuoustime periodic stochastic systems by feedback control based on periodic discretetime observations. Mathematical Control & Related Fields, 2019 doi: 10.3934/mcrf.2020017 
[7] 
Ferenc A. Bartha, Ábel Garab. Necessary and sufficient condition for the global stability of a delayed discretetime single neuron model. Journal of Computational Dynamics, 2014, 1 (2) : 213232. doi: 10.3934/jcd.2014.1.213 
[8] 
Elena K. Kostousova. On polyhedral estimates for trajectory tubes of dynamical discretetime systems with multiplicative uncertainty. Conference Publications, 2011, 2011 (Special) : 864873. doi: 10.3934/proc.2011.2011.864 
[9] 
Qingling Zhang, Guoliang Wang, Wanquan Liu, Yi Zhang. Stabilization of discretetime Markovian jump systems with partially unknown transition probabilities. Discrete & Continuous Dynamical Systems  B, 2011, 16 (4) : 11971211. doi: 10.3934/dcdsb.2011.16.1197 
[10] 
Byungik Kahng, Miguel Mendes. The characterization of maximal invariant sets of nonlinear discretetime control dynamical systems. Conference Publications, 2013, 2013 (special) : 393406. doi: 10.3934/proc.2013.2013.393 
[11] 
Zhongkui Li, Zhisheng Duan, Guanrong Chen. Consensus of discretetime linear multiagent systems with observertype protocols. Discrete & Continuous Dynamical Systems  B, 2011, 16 (2) : 489505. doi: 10.3934/dcdsb.2011.16.489 
[12] 
Deepak Kumar, Ahmad Jazlan, Victor Sreeram, Roberto Togneri. Partial fraction expansion based frequency weighted model reduction for discretetime systems. Numerical Algebra, Control & Optimization, 2016, 6 (3) : 329337. doi: 10.3934/naco.2016015 
[13] 
Hongyan Yan, Yun Sun, Yuanguo Zhu. A linearquadratic control problem of uncertain discretetime switched systems. Journal of Industrial & Management Optimization, 2017, 13 (1) : 267282. doi: 10.3934/jimo.2016016 
[14] 
Elena K. Kostousova. On control synthesis for uncertain dynamical discretetime systems through polyhedral techniques. Conference Publications, 2015, 2015 (special) : 723732. doi: 10.3934/proc.2015.0723 
[15] 
Yuefen Chen, Yuanguo Zhu. Indefinite LQ optimal control with process state inequality constraints for discretetime uncertain systems. Journal of Industrial & Management Optimization, 2018, 14 (3) : 913930. doi: 10.3934/jimo.2017082 
[16] 
Elena K. Kostousova. On polyhedral control synthesis for dynamical discretetime systems under uncertainties and state constraints. Discrete & Continuous Dynamical Systems  A, 2018, 38 (12) : 61496162. doi: 10.3934/dcds.2018153 
[17] 
Victor Kozyakin. Minimax joint spectral radius and stabilizability of discretetime linear switching control systems. Discrete & Continuous Dynamical Systems  B, 2019, 24 (8) : 35373556. doi: 10.3934/dcdsb.2018277 
[18] 
Mats Gyllenberg, Jifa Jiang, Lei Niu, Ping Yan. Permanence and universal classification of discretetime competitive systems via the carrying simplex. Discrete & Continuous Dynamical Systems  A, 2020, 40 (3) : 16211663. doi: 10.3934/dcds.2020088 
[19] 
Xi Zhu, Meixia Li, Chunfa Li. Consensus in discretetime multiagent systems with uncertain topologies and random delays governed by a Markov chain. Discrete & Continuous Dynamical Systems  B, 2020 doi: 10.3934/dcdsb.2020111 
[20] 
Yueyuan Zhang, Yanyan Yin, Fei Liu. Robust observerbased control for discretetime semiMarkov jump systems with actuator saturation. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020105 
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]