Solution of jump parameter systems of differential and difference equations with semi-Markov coefficients

2003 ◽  
Vol 40 (2) ◽  
pp. 442-454 ◽  
Author(s):  
Efraim Shmerling ◽  
Kenneth J. Hochberg
Keyword(s):  
Asymptotic Stability ◽  
Markov Process ◽  
Difference Equations ◽  
The State ◽  
Systems Of Equations ◽  
Moment Equations ◽  
Semi Markov Process

We study linear jump parameter systems of differential and difference equations whose coefficients depend on the state of a semi-Markov process. We derive systems of equations for the first two moments of the random solutions of these jump parameter systems, and illustrate how moment equations can be used in examining their asymptotic stability.

Solution of jump parameter systems of differential and difference equations with semi-Markov coefficients

2003 ◽  
Vol 40 (02) ◽  
pp. 442-454 ◽  
Author(s):  
Efraim Shmerling ◽  
Kenneth J. Hochberg
Keyword(s):  
Asymptotic Stability ◽  
Markov Process ◽  
Difference Equations ◽  
The State ◽  
Systems Of Equations ◽  
Moment Equations ◽  
Semi Markov Process

We study linear jump parameter systems of differential and difference equations whose coefficients depend on the state of a semi-Markov process. We derive systems of equations for the first two moments of the random solutions of these jump parameter systems, and illustrate how moment equations can be used in examining their asymptotic stability.

scholarly journals Possibility of Application of the Theory of Semi-Markov Processes to Determine Reliability of Diagnosing Systems / MOŻLIWOŚĆ ZASTOSOWANIA TEORII PROCESÓW SEMI-MARKOWA DO OKREŚLENIA NIEZAWODNOŚCI SYSTEMÓW DIAGNOZUJĄCYCH

2012 ◽  
Vol 24 (1) ◽  
pp. 49-58 ◽  
Author(s):  
Jerzy Girtler
Keyword(s):  
Markov Process ◽  
Markov Processes ◽  
Continuous Time ◽  
Diagnostic Tests ◽  
The State ◽  
Actual State ◽  
Reliability Model ◽  
Discrete State ◽  
Semi Markov Process ◽  
Semi Markov Processes

Abstract The paper provides justification for the necessity to define reliability of diagnosing systems (SDG) in order to develop a diagnosis on state of any technical mechanism being a diagnosed system (SDN). It has been shown that the knowledge of SDG reliability enables defining diagnosis reliability. It has been assumed that the diagnosis reliability can be defined as a diagnosis property which specifies the degree of recognizing by a diagnosing system (SDG) the actual state of the diagnosed system (SDN) which may be any mechanism, and the conditional probability p(S*/K*) of occurrence (existence) of state S* of the mechanism (SDN) as a diagnosis measure provided that at a specified reliability of SDG, the vector K* of values of diagnostic parameters implied by the state, is observed. The probability that SDG is in the state of ability during diagnostic tests and the following diagnostic inferences leading to development of a diagnosis about the SDN state, has been accepted as a measure of SDG reliability. The theory of semi-Markov processes has been used for defining the SDG reliability, that enabled to develop a SDG reliability model in the form of a seven-state (continuous-time discrete-state) semi-Markov process of changes of SDG states.

scholarly journals Moment Equations in Modeling a Stable Foreign Currency Exchange Market in Conditions of Uncertainty

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Josef Diblík ◽  
Irada Dzhalladova ◽  
Mária Michalková ◽  
Miroslava Růžičková
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Markov Process ◽  
Linear Differential Equation ◽  
Foreign Currency ◽  
Exchange Market ◽  
Moment Equations ◽  
Currency Exchange ◽  
Semi Markov Process ◽  
Linear Differential

The paper develops a mathematical model of foreign currency exchange market in the form of a stochastic linear differential equation with coefficients depending on a semi-Markov process. The boundaries of the domain of its instability is determined by using moment equations.

scholarly journals The Renewal Process Generated By Return Times of Semi-Markov Process in Reliability Models

2017 ◽  
Vol 43 (1) ◽  
pp. 365-380
Author(s):  
Franciszek Grabski
Keyword(s):  
Markov Process ◽  
Renewal Process ◽  
First Passage Time ◽  
Return Time ◽  
Passage Time ◽  
Reliability Theory ◽  
Systems Of Equations ◽  
Reliability Models ◽  
Return Times ◽  
Semi Markov Process

Abstract The renewal process generated by the return times of semi-Markov process to a given state is considered in the paper. The return time to a state j and also a first passage time from a given state i to the state j of semi-Markov process are basic concepts that are used to determine this process. The systems of equations for distributions, expectations and secondond moments of these random variables are presented. Theorem concerning the asymptotic distribution of the considered renewal process is presented in this article. Moreover an illustrative example from the reliability theory is presented in the paper.

Sufficient optimality conditions for control-limit policy in a semi-Markov process

1976 ◽  
Vol 13 (2) ◽  
pp. 400-406 ◽  
Author(s):  
I. Gertsbach
Keyword(s):  
Markov Chain ◽  
Markov Process ◽  
Optimality Conditions ◽  
Hazard Rate ◽  
The State ◽  
Control Limit ◽  
Sufficient Optimality Conditions ◽  
Finite State ◽  
Semi Markov Process ◽  
Rate Property

A finite-state semi-Markov process (SMP) with penalties is considered. A property which is similar to an increasing-hazard-rate property for a Markov chain is defined for an SMP. The SMP is controlled by shifts from the state Ei to immediately after a transition has occurred. Conditions are given which guarantee that the optimal stationary Markovian policy belongs to a subclass of control-limit policies.

Sufficient optimality conditions for control-limit policy in a semi-Markov process

1976 ◽  
Vol 13 (02) ◽  
pp. 400-406 ◽  
Author(s):  
I. Gertsbach
Keyword(s):  
Markov Chain ◽  
Markov Process ◽  
Optimality Conditions ◽  
Hazard Rate ◽  
The State ◽  
Control Limit ◽  
Sufficient Optimality Conditions ◽  
Finite State ◽  
Semi Markov Process ◽  
Rate Property

A finite-state semi-Markov process (SMP) with penalties is considered. A property which is similar to an increasing-hazard-rate property for a Markov chain is defined for an SMP. The SMP is controlled by shifts from the state Ei to immediately after a transition has occurred. Conditions are given which guarantee that the optimal stationary Markovian policy belongs to a subclass of control-limit policies.

scholarly journals Event-Triggering State and Fault Estimation for a Class of Nonlinear Systems Subject to Sensor Saturations

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1242
Author(s):  
Cong Huang ◽  
Bo Shen ◽  
Lei Zou ◽  
Yuxuan Shen
Keyword(s):  
Nonlinear Systems ◽  
Difference Equations ◽  
Estimation Error ◽  
Upper Bounds ◽  
The State ◽  
Fault Estimation ◽  
Triggering Mechanism ◽  
Transmission Frequency ◽  
Current Transmission ◽  
Event Triggering

This paper is concerned with the state and fault estimation issue for nonlinear systems with sensor saturations and fault signals. For the sake of avoiding the communication burden, an event-triggering protocol is utilized to govern the transmission frequency of the measurements from the sensor to its corresponding recursive estimator. Under the event-triggering mechanism (ETM), the current transmission is released only when the relative error of measurements is bigger than a prescribed threshold. The objective of this paper is to design an event-triggering recursive state and fault estimator such that the estimation error covariances for the state and fault are both guaranteed with upper bounds and subsequently derive the gain matrices minimizing such upper bounds, relying on the solutions to a set of difference equations. Finally, two experimental examples are given to validate the effectiveness of the designed algorithm.

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