scholarly journals A necessary and sufficient condition for robust asymptotic stabilizability of continuous-time uncertain switched linear systems

2004 ◽  
Author(s):  
H. Lin ◽  
P.J. Antsaklis
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Switched Linear Systems ◽  
Necessary And Sufficient

On the relationship between µ-invariant measures and quasi-stationary distributions for continuous-time Markov chains

1993 ◽  
Vol 25 (01) ◽  
pp. 82-102
Author(s):  
M. G. Nair ◽  
P. K. Pollett
Keyword(s):  
Invariant Measure ◽  
Stationary Distribution ◽  
Continuous Time ◽  
Sufficient Condition ◽  
Transition Rates ◽  
Necessary And Sufficient Condition ◽  
Absorbing State ◽  
Necessary And Sufficient ◽  
Forward Equations ◽  
Quasi Stationary Distribution

In a recent paper, van Doorn (1991) explained how quasi-stationary distributions for an absorbing birth-death process could be determined from the transition rates of the process, thus generalizing earlier work of Cavender (1978). In this paper we shall show that many of van Doorn's results can be extended to deal with an arbitrary continuous-time Markov chain over a countable state space, consisting of an irreducible class, C, and an absorbing state, 0, which is accessible from C. Some of our results are extensions of theorems proved for honest chains in Pollett and Vere-Jones (1992). In Section 3 we prove that a probability distribution on C is a quasi-stationary distribution if and only if it is a µ-invariant measure for the transition function, P. We shall also show that if m is a quasi-stationary distribution for P, then a necessary and sufficient condition for m to be µ-invariant for Q is that P satisfies the Kolmogorov forward equations over C. When the remaining forward equations hold, the quasi-stationary distribution must satisfy a set of ‘residual equations' involving the transition rates into the absorbing state. The residual equations allow us to determine the value of µ for which the quasi-stationary distribution is µ-invariant for P. We also prove some more general results giving bounds on the values of µ for which a convergent measure can be a µ-subinvariant and then µ-invariant measure for P. The remainder of the paper is devoted to the question of when a convergent µ-subinvariant measure, m, for Q is a quasi-stationary distribution. Section 4 establishes a necessary and sufficient condition for m to be a quasi-stationary distribution for the minimal chain. In Section 5 we consider ‘single-exit' chains. We derive a necessary and sufficient condition for there to exist a process for which m is a quasi-stationary distribution. Under this condition all such processes can be specified explicitly through their resolvents. The results proved here allow us to conclude that the bounds for µ obtained in Section 3 are, in fact, tight. Finally, in Section 6, we illustrate our results by way of two examples: regular birth-death processes and a pure-birth process with absorption.

scholarly journals Controllability of Linear Discrete-Time Systems with Both Delayed States and Delayed Inputs

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Hong Shi ◽  
Guangming Xie ◽  
Wenguang Luo
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Control Delay ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
And Control ◽  
Time Systems ◽  
Time Linear

The controllability issues for discrete-time linear systems with delay in state and control are addressed. By introducing a new concept, the controllability realization index (CRI), the characteristic of controllability is revealed. An easily testable necessary and sufficient condition for the controllability of discrete-time linear systems with state and control delay is established.

scholarly journals Positifitas dan Ketercapaian Sistem Linier Fractional Waktu Kontinu

CAUCHY ◽  
2011 ◽  
Vol 2 (1) ◽  
pp. 18
Author(s):  
Imam Fahcruddin
Keyword(s):  
Continuous Time ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Positive Systems ◽  
Necessary And Sufficient Condition ◽  
Fractional Systems ◽  
Necessary And Sufficient

<div class="standard"><a id="magicparlabel-2384">This paper studies a solution of the fractional continuous-time linier system. Necessary and sufficient condition were established for the internal and external positivity of fractional systems. Sufficient conditions are given for the reachability of fractional positive systems. </a></div>

On the identification of continuous-time Markov chains with a given invariant measure

1994 ◽  
Vol 31 (04) ◽  
pp. 897-910
Author(s):  
P. K. Pollett
Keyword(s):  
Invariant Measure ◽  
Continuous Time ◽  
Branching Process ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Birth Process ◽  
Continuous Time Markov Chains ◽  
Branching Process With Immigration ◽  
Birth Processes ◽  
Necessary And Sufficient

In [14] a necessary and sufficient condition was obtained for there to exist uniquely a Q-process with a specified invariant measure, under the assumption that Q is a stable, conservative, single-exit matrix. The purpose of this note is to demonstrate that, for an arbitrary stable and conservative q-matrix, the same condition suffices for the existence of a suitable Q-process, but that this process might not be unique. A range of examples is considered, including pure-birth processes, a birth process with catastrophes, birth-death processes and the Markov branching process with immigration.

scholarly journals Consensus of Third-Order Multiagent Systems with Time Delay in Undirected Networks

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Yanfen Cao ◽  
Yuangong Sun
Keyword(s):  
Time Delay ◽  
Multiagent Systems ◽  
Continuous Time ◽  
Matrix Analysis ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Third Order ◽  
Necessary And Sufficient ◽  
Frequency Domain Approach ◽  
Order Continuous

We consider consensus of a class of third-order continuous-time multiagent systems with time delay in undirected networks. By using matrix analysis and a frequency domain approach, a necessary and sufficient condition for consensus is established. A simulation result is also given to illustrate the main theoretical result.

On the Problem of Establishing the Existence of Stationary Distributions for Continuous-Time Markov Chains

1993 ◽  
Vol 7 (4) ◽  
pp. 529-543 ◽  
Author(s):  
P. K. Pollett ◽  
P. G. Taylor
Keyword(s):  
Markov Chains ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Transition Rates ◽  
Necessary And Sufficient Condition ◽  
Stationary Distributions ◽  
Continuous Time Markov Chains ◽  
Necessary And Sufficient ◽  
Networks Of Queues

We consider the problem of establishing the existence of stationary distributions for continuous-time Markov chains directly from the transition rates Q. Given an invariant probability distribution m for Q, we show that a necessary and sufficient condition for m to be a stationary distribution for the minimal process is that Q be regular. We provide sufficient conditions for the regularity of Q that are simple to verify in practice, thus allowing one to easily identify stationary distributions for a variety of models. To illustrate our results, we shall consider three classes of multidimensional Markov chains, namely, networks of queues with batch movements, semireversible queues, and partially balanced Markov processes.

Normal and Quasi-Normal Modes in Damped Linear Dynamic Systems

1966 ◽  
Vol 33 (2) ◽  
pp. 413-416 ◽  
Author(s):  
J. S. Maybee
Keyword(s):  
Linear Systems ◽  
Dynamic Systems ◽  
Normal Modes ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Linear Dynamic Systems ◽  
Linear Dynamic ◽  
Necessary And Sufficient

A generalization of the concept of classical normal modes in damped linear systems is presented. It is then shown that a necessary and sufficient condition that such quasi-normal modes exist is that certain matrices associated with the system commute. Necessary and sufficient conditions of the same type are also obtained for the classical normal modes, but under more restrictive conditions.

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