Stochastic stability properties of jump linear systems Export

@article{Feng_TAC92, abstract = {Jump linear systems are defined as a family of linear systems with randomly jumping parameters (usually governed by a Markov jump process) and are used to model systems subject to failures or changes in structure. The authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties. It is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability, and a testable necessary and sufficient condition for second moment stability is derived. The Lyapunov exponent method for the study of almost sure sample stability is discussed, and a theorem which characterizes the Lyapunov exponents of jump linear systems is presented. Finally, for one-dimensional jump linear system, it is proved that the region for \δ-moment stability is monotonically converging to the region for almost sure stability at \δ\↓0⁺}, author = {Feng, X. and Loparo, K. A. and Ji, Y. and Chizeck, H. J.}, booktitle = {Automatic Control, IEEE Transactions on}, citeulike-article-id = {4505442}, citeulike-linkout-0 = {http://dx.doi.org/10.1109/9.109637}, citeulike-linkout-1 = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=109637}, doi = {10.1109/9.109637}, journal = {Automatic Control, IEEE Transactions on}, keywords = {jump\_processes\_random\_networks, lqg\_lqr, optimal\_control, stochastic\_control}, number = {1}, pages = {38--53}, posted-at = {2009-05-12 17:24:44}, priority = {2}, title = {Stochastic stability properties of jump linear systems}, url = {http://dx.doi.org/10.1109/9.109637}, volume = {37}, year = {1992} }

TY - JOUR ID - Feng_TAC92 L3 - citeulike-article-id:4505442 N2 - Jump linear systems are defined as a family of linear systems with randomly jumping parameters (usually governed by a Markov jump process) and are used to model systems subject to failures or changes in structure. The authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties. It is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability, and a testable necessary and sufficient condition for second moment stability is derived. The Lyapunov exponent method for the study of almost sure sample stability is discussed, and a theorem which characterizes the Lyapunov exponents of jump linear systems is presented. Finally, for one-dimensional jump linear system, it is proved that the region for δ-moment stability is monotonically converging to the region for almost sure stability at δ↓0⁺ IS - 1 JF - Automatic Control, IEEE Transactions on EP - 53 TI - Stochastic stability properties of jump linear systems VL - 37 T2 - Automatic Control, IEEE Transactions on SP - 38 KW - jump_processes_random_networks KW - lqg_lqr KW - optimal_control KW - stochastic_control AU - Feng, X AU - Loparo, KA AU - Ji, Y AU - Chizeck, HJ PY - 1992/// UR - http://dx.doi.org/10.1109/9.109637 ER -