Stochastic stability and stabilization of state-dependent jump linear system

2013 ◽  
Author(s):  
Shaikshavali Chitraganti ◽  
Samir Aberkane ◽  
Christophe Aubrun
Keyword(s):  
Linear System ◽  
Stochastic Stability ◽  
State Dependent ◽  
Stability And Stabilization

scholarly journals Stability and stabilization of linear positive systems on time scales

Positivity ◽  
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 ◽  
Necessary And Sufficient

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.

The Optimal Regulator Problem for a Stationary Linear System With State-Dependent Noise

1970 ◽  
Vol 92 (2) ◽  
pp. 363-368 ◽  
Author(s):  
P. J. McLane
Keyword(s):  
Linear System ◽  
Sufficient Conditions ◽  
Quadratic Functional ◽  
Optimal Controls ◽  
Final Time ◽  
State Dependent ◽  
Continuous Dynamic ◽  
The Stability ◽  
And Control ◽  
Stationary Linear System

The problem of minimizing a quadratic functional of the system outputs and control for a stationary linear system with state-dependent noise is solved in this paper. Both the finite final time and infinite final time versions of the problem are treated. For the latter case existence conditions are obtained using the second method of Lyapunov. The optimal controls for both problems are obtained using Bellman’s continuous dynamic programming. In light of this, the system dynamics are assumed to determine a diffusion process. For the infinite final time version of the problem noted above, sufficient conditions are obtained for the stability of the optimal system and uniqueness of the optimal control law. In addition, for this problem, an example is treated. The computational results for this example illustrate some of the qualitative features of regulators for linear, stationary systems with state-dependent disturbances.

scholarly journals Stochastic stability of some state-dependent growth-collapse processes

2007 ◽  
Vol 39 (01) ◽  
pp. 189-220
Author(s):  
Christian Y. Robert
Keyword(s):  
Random Walk ◽  
Discrete Time ◽  
Power Law ◽  
Stochastic Stability ◽  
Long Range Dependence ◽  
Time Process ◽  
Power Law Distribution ◽  
State Dependent ◽  
Dependent Growth ◽  
Collapse Process

In this paper we consider a discrete-time process which grows according to a random walk with nonnegative increments between crash times at which it collapses to 0. We assume that the probability of crashing depends on the level of the process. We study the stochastic stability of this growth-collapse process. Special emphasis is given to the case in which the probability of crashing tends to 0 as the level of the process increases. In particular, we show that the process may exhibit long-range dependence and that the crash sizes may have a power law distribution.

scholarly journals Delay-dependent stability and stabilization of uncertain discrete-time markovian jump singular systems with time delay

2007 ◽  
Vol 49 (1) ◽  
pp. 111-129 ◽  
Author(s):  
Shuping Ma ◽  
Xinzhi Liu ◽  
Chenghui Zhang
Keyword(s):  
Time Delay ◽  
Linear Matrix Inequalities ◽  
Discrete Time ◽  
Stochastic Stability ◽  
Singular Systems ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Markovian Jump ◽  
Stability And Stabilization ◽  
Delay Dependent

This paper discusses robust stochastic stability and stabilization of time-delay discrete Markovian jump singular systems with parameter uncertainties. Based on the restricted system equivalent (RES) transformation, a delay-dependent linear matrix inequalities condition for time-delay discrete-time Markovian jump singular systems to be regular, causal and stochastically stable is established. With this condition, problems of robust stochastic stability and stabilization are solved, and delay-dependent linear matrix inequalities are obtained. A numerical example is also given to illustrate the effectiveness of this method.2000Mathematics subject classification: primary 39A12; secondary 93C55.

scholarly journals Stochastic stability of some state-dependent growth-collapse processes

2007 ◽  
Vol 39 (1) ◽  
pp. 189-220 ◽  
Author(s):  
Christian Y. Robert
Keyword(s):  
Random Walk ◽  
Discrete Time ◽  
Power Law ◽  
Stochastic Stability ◽  
Long Range Dependence ◽  
Time Process ◽  
Power Law Distribution ◽  
State Dependent ◽  
Dependent Growth ◽  
Collapse Process

In this paper we consider a discrete-time process which grows according to a random walk with nonnegative increments between crash times at which it collapses to 0. We assume that the probability of crashing depends on the level of the process. We study the stochastic stability of this growth-collapse process. Special emphasis is given to the case in which the probability of crashing tends to 0 as the level of the process increases. In particular, we show that the process may exhibit long-range dependence and that the crash sizes may have a power law distribution.

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