Stabilization for a Class of Discrete-Time Switched Linear Singular Systems

2011 ◽  
Vol 480-481 ◽  
pp. 1406-1411 ◽  
Author(s):  
Bo Men ◽  
Xiao Song Li ◽  
Xin Yuan Ou
Keyword(s):  
Lyapunov Function ◽  
State Space ◽  
Discrete Time ◽  
Continuous Time ◽  
Singular Systems ◽  
Stabilization Problem ◽  
Switching Law ◽  
Multiple Lyapunov Function ◽  
Hybrid Switching

In this paper, the stabilization problem is studied by using multiple Lyapunov function techniques for a class of discrete-time switched linear singular (DSLS) systems. The existing criteria of stability for continuous-time switched singular systems are extended into DSLS systems. Then, a hybrid switching law is designed based on a partition of state space by using S-procedure method.

Stability and L2–Gain analysis of linear switched singular systems by using multiple discontinuous Lyapunov function approach

2019 ◽  
Vol 41 (15) ◽  
pp. 4197-4206 ◽  
Author(s):  
Jumei Wei ◽  
Huimin Zhi ◽  
Kai Liu
Keyword(s):  
Lyapunov Function ◽  
Exponential Stability ◽  
Discrete Time ◽  
Text Analysis ◽  
Dwell Time ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Function Approach ◽  
Discrete Time Case

In this paper, the problem of the E-exponential stability and [Formula: see text] analysis of linear switched singular systems is investigated in discrete-time case. By using a multiple discontinuous Lyapunov function approach and adopting the mode-dependent average dwell time (MDADT) switching signals, new sufficient conditions of E-exponential stability and [Formula: see text] analysis for linear switched singular systems are presented. Based on the above results, we also derive the weighted [Formula: see text] performance index. In addition, by utilizing our proposed method, tighter bounds on average dwell time can be obtained for our considered systems. At last, a numerical example is given to show the effectiveness of the results.

Asymptotic behaviour of continuous time, continuous state-space branching processes

1974 ◽  
Vol 11 (04) ◽  
pp. 669-677 ◽  
Author(s):  
D. R. Grey
Keyword(s):  
Asymptotic Behaviour ◽  
State Space ◽  
Discrete Time ◽  
Continuous Time ◽  
Branching Processes ◽  
Discrete State ◽  
Space And Time ◽  
Continuous State Space ◽  
Continuous State ◽  
Discrete State Space

Results on the behaviour of Markov branching processes as time goes to infinity, hitherto obtained for models which assume a discrete state-space or discrete time or both, are here generalised to a model with both state-space and time continuous. The results are similar but the methods not always so.

scholarly journals Stability Results of a Class of Hybrid Systems under Switched Continuous-Time and Discrete-Time Control

2009 ◽  
Vol 2009 ◽  
pp. 1-28 ◽  
Author(s):  
M. De la Sen ◽  
A. Ibeas
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Linear Time ◽  
Sampling Period ◽  
Switched System ◽  
Time Interval ◽  
Stabilizing Controller ◽  
Switching Law ◽  
Discrete Dynamic System ◽  
Time Control

This paper investigates the stability properties of a class of switched systems possessing several linear time-invariant parameterizations (or configurations) which are governed by a switching law. It is assumed that the parameterizations are stabilized individually via an appropriate linear state or output feedback stabilizing controller whose existence is first discussed. A main novelty with respect to previous research is that the various individual parameterizations might be continuous-time, discrete-time, or mixed so that the whole switched system is a hybrid continuous/discrete dynamic system. The switching rule governs the choice of the parameterization which is active at each time interval in the switched system. Global asymptotic stability of the switched system is guaranteed for the case when a common Lyapunov function exists for all the individual parameterizations and the sampling period of the eventual discretized parameterizations taking part of the switched system is small enough. Some extensions are also investigated for controlled systems under decentralized or mixed centralized/decentralized control laws which stabilize each individual active parameterization.

A SUCCESSIVE LUMPING PROCEDURE FOR A CLASS OF MARKOV CHAINS

2012 ◽  
Vol 26 (4) ◽  
pp. 483-508 ◽  
Author(s):  
Michael N. Katehakis ◽  
Laurens C. Smit
Keyword(s):  
Markov Chains ◽  
State Space ◽  
Markov Processes ◽  
Discrete Time ◽  
Continuous Time ◽  
Queueing Models ◽  
Semi Markov Processes ◽  
Stationary Probabilities

A class of Markov chains we call successively lumbaple is specified for which it is shown that the stationary probabilities can be obtained by successively computing the stationary probabilities of a propitiously constructed sequence of Markov chains. Each of the latter chains has a(typically much) smaller state space and this yields significant computational improvements. We discuss how the results for discrete time Markov chains extend to semi-Markov processes and continuous time Markov processes. Finally, we will study applications of successively lumbaple Markov chains to classical reliability and queueing models.

Asymptotic Stability Analysis and Controller Design for a Class of Switched Uncertain Singular Systems with Time-Delay

2013 ◽  
Vol 385-386 ◽  
pp. 890-895
Author(s):  
Yue Sheng Luo ◽  
Shan Gao ◽  
Yang Gao ◽  
Tong Li ◽  
Chun Fang Liu
Keyword(s):  
Time Delay ◽  
Asymptotic Stability ◽  
Lyapunov Function ◽  
Controller Design ◽  
Singular Systems ◽  
Singular System ◽  
Equivalent Transformation ◽  
Switching Law ◽  
Uncertain Singular Systems ◽  
Delay Dependent

The problem of robustly asymptotic stability and controller design for a class of switched uncertain singular systems with time-delay is considered. By means of Lyapunov function and Matrix equivalent transformation, based on multiple Lyapunov function techniques, a delay-dependent sufficient condition is deduced, such that the solution of the switched singular system with time-delay is robustly asymptotic stable for all admissible uncertainties under an appropriate switching law. Furthermore, a convex optimization problem with LMI constraints is formulated such that the maximum bound on the admissible delay can be determined by using the LMI toolbox in MATLAB. Finally, an illustrative example is given to demonstrate the effectiveness of proposed method.

scholarly journals Exact and approximate hidden Markov chain filters based on discrete observations

2015 ◽  
Vol 32 (3-4) ◽  
pp. 159-176
Author(s):  
Nicole Bäuerle ◽  
Igor Gilitschenski ◽  
Uwe Hanebeck
Keyword(s):  
Markov Chain ◽  
State Space ◽  
Discrete Time ◽  
Continuous Time ◽  
Hidden Markov ◽  
Numerical Study ◽  
Recursion Formula ◽  
The State ◽  
Continuous Time Markov Chain ◽  
Discrete Observations

Abstract We consider a Hidden Markov Model (HMM) where the integrated continuous-time Markov chain can be observed at discrete time points perturbed by a Brownian motion. The aim is to derive a filter for the underlying continuous-time Markov chain. The recursion formula for the discrete-time filter is easy to derive, however involves densities which are very hard to obtain. In this paper we derive exact formulas for the necessary densities in the case the state space of the HMM consists of two elements only. This is done by relating the underlying integrated continuous-time Markov chain to the so-called asymmetric telegraph process and by using recent results on this process. In case the state space consists of more than two elements we present three different ways to approximate the densities for the filter. The first approach is based on the continuous filter problem. The second approach is to derive a PDE for the densities and solve it numerically. The third approach is a crude discrete time approximation of the Markov chain. All three approaches are compared in a numerical study.

Asymptotic behaviour of continuous time, continuous state-space branching processes

1974 ◽  
Vol 11 (4) ◽  
pp. 669-677 ◽  
Author(s):  
D. R. Grey
Keyword(s):  
Asymptotic Behaviour ◽  
State Space ◽  
Discrete Time ◽  
Continuous Time ◽  
Branching Processes ◽  
Discrete State ◽  
Space And Time ◽  
Continuous State Space ◽  
Continuous State ◽  
Discrete State Space

Results on the behaviour of Markov branching processes as time goes to infinity, hitherto obtained for models which assume a discrete state-space or discrete time or both, are here generalised to a model with both state-space and time continuous. The results are similar but the methods not always so.

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