Necessary and Sufficient Conditions for Stochastic Stability and Stabilization of Positive Systems With Two Independent Markov Processes

The Relationship

This paper is concerned with the relationship between insensitivity in a certain class of Markov processes and properties of that process when time is reversed. Necessary and sufficient conditions for insensitivity are established and linked to already proved results. A number of examples of insensitive systems are given.

Stability and stabilization of linear positive systems on time scales

Positivity ◽

10.1007/s11117-020-00735-z ◽

2020 ◽

Vol 24 (5) ◽

pp. 1361-1372

Author(s):

Zbigniew Bartosiewicz

Keyword(s):

Control System ◽

Linear System ◽

Time Scale ◽

Sufficient Conditions ◽

Positive Control ◽

Positive Systems ◽

The Matrix ◽

Exponentially Stable ◽

Stability And Stabilization ◽

Abstract It is shown that a positive linear system on a time scale with a bounded graininess is uniformly exponentially stable if and only if the characteristic polynomial of the matrix defining the system has all its coefficients positive. Then this fact is used to find necessary and sufficient conditions of positive stabilizability of a positive control system on a time scale.

$L_1$-Stochastic Stability and $L_1$-Gain Performance of Positive Markov Jump Linear Systems With Time-Delays: Necessary and Sufficient Conditions

IEEE Transactions on Automatic Control ◽

10.1109/tac.2017.2671035 ◽

2017 ◽

Vol 62 (7) ◽

pp. 3634-3639 ◽

Cited By ~ 38

Author(s):

Shuqian Zhu ◽

Qing-Long Han ◽

Chenghui Zhang

Keyword(s):

Linear Systems ◽

Stochastic Stability ◽

Time Delays ◽

Sufficient Conditions ◽

Markov Jump ◽

Jump Linear Systems ◽

Markov Jump Linear Systems ◽

Insensitivity and reversed Markov processes

Advances in Applied Probability ◽

10.1017/s0001867800021595 ◽

1983 ◽

Vol 15 (04) ◽

pp. 752-768 ◽

Cited By ~ 9

Author(s):

W. Henderson

Keyword(s):

Markov Processes ◽

Sufficient Conditions ◽

The Relationship

This paper is concerned with the relationship between insensitivity in a certain class of Markov processes and properties of that process when time is reversed. Necessary and sufficient conditions for insensitivity are established and linked to already proved results. A number of examples of insensitive systems are given.

Necessary and sufficient conditions on the parameters of 1-D Gaussian Markov processes

IEEE Transactions on Signal Processing ◽

10.1109/78.134491 ◽

1992 ◽

Vol 40 (5) ◽

pp. 1266-1271 ◽

Cited By ~ 8

Author(s):

S. Lakshmanan ◽

K. Derin

Keyword(s):

Markov Processes ◽

Sufficient Conditions ◽

Weak convergence of first-rare-event times for semi-Markov processes

10.31219/osf.io/q95cv ◽

2020 ◽

Author(s):

AISDL

Keyword(s):

Weak Convergence ◽

Markov Processes ◽

Sufficient Conditions ◽

Rare Event ◽

Finite Set ◽

In Series ◽

Event Times ◽

Semi Markov Processes ◽

Necessary and sufficient conditions for weak convergence of first-rareevent times for semi-Markov processes with finite set of states in series of schemes are obtained.

Necessary and Sufficient Conditions for Weak Convergence of One-Dimensional Markov Processes

The Dynkin Festschrift ◽

10.1007/978-1-4612-0279-0_4 ◽

1994 ◽

pp. 95-109 ◽

Cited By ~ 5

Author(s):

Mark I. Freidlin ◽

Alexander D. Wentzell

Keyword(s):

Weak Convergence ◽

Markov Processes ◽

Sufficient Conditions ◽

One Dimensional ◽

COPULA-BASED CHARACTERIZATIONS FOR HIGHER ORDER MARKOV PROCESSES

Econometric Theory ◽

10.1017/s0266466609090720 ◽

2009 ◽

Vol 25 (3) ◽

pp. 819-846 ◽

Cited By ~ 58

Author(s):

Rustam Ibragimov

Keyword(s):

Time Series ◽

Markov Processes ◽

Sufficient Conditions ◽

Higher Order ◽

Conditional Symmetry ◽

Finite Dimensional ◽

Dependence Properties

In this paper, we obtain characterizations of higher order Markov processes in terms of copulas corresponding to their finite-dimensional distributions. The results are applied to establish necessary and sufficient conditions for Markov processes of a given order to exhibitm-dependence,r-independence, or conditional symmetry. The paper also presents a study of applicability and limitations of different copula families in constructing higher order Markov processes with the preceding dependence properties. We further introduce new classes of copulas that allow one to combine Markovness withm-dependence orr-independence in time series.

Necessary and sufficient conditions for bounded control of positive systems

2008 International Conference on Communications, Circuits and Systems ◽

10.1109/icccas.2008.4657974 ◽

2008 ◽

Author(s):

Xingwen Liu

Keyword(s):

Sufficient Conditions ◽

Positive Systems ◽

Bounded Control ◽

Stabilization of positive descriptor fractional discrete-time linear system with two different fractional orders by decentralized controller

Bulletin of the Polish Academy of Sciences Technical Sciences ◽

10.1515/bpasts-2017-0076 ◽

2017 ◽

Vol 65 (5) ◽

pp. 709-714 ◽

Cited By ~ 1

Author(s):

Ł. Sajewski

Keyword(s):

Linear System ◽

Linear Systems ◽

Discrete Time ◽

Sufficient Conditions ◽

Positive Systems ◽

Numerical Example ◽

Fractional Orders ◽

Time Linear

Abstract Positive descriptor fractional discrete-time linear systems with fractional different orders are addressed in the paper. The decomposition of the regular pencil is used to extend necessary and sufficient conditions for positivity of the descriptor fractional discrete-time linear system with different fractional orders. A method for finding the decentralized controller for the class of positive systems is proposed and its effectiveness is demonstrated on a numerical example.