Stochastic Stability and Control

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Remark 2. In the next section we will turn the attention to the class of SNS 3 and provide some results related to the stability in probability of this system. In this section, where the dynamics f t , 0 and g t , 0 may be non-vanishing at the origin, we study the stability in probability of nontrivial solutions of SNS 3. In the following theorem that is an extension of Theorem 3. Then the following three statements are equivalent :.

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Therefore, Definition 2. Without any loss of generality, assume.

Then using 5 and 6 and by applying the converse result of Theorem 3. Taking into account 10 and 13 - 14 yields. Therefore, from 20 and Definition 2.

SIAM Journal on Control and Optimization

This completes the proof of Theorem 3. Many authors have paid attention to the subject of stability in probability of trivial solutions of stochastic systems in the past years. On the other hand, it is known that there are many types of stochastic systems all of whose solutions tend to each other although they do not have the trivial solution. In this paper, we have established the stability in probability of nontrivial solutions for SNS 3. We have derived a stochastic version of CLF and provided the necessary and sufficient conditions for stability in probability of a nontrivial solution for SNS 3.

Stochastic Stability and Control (Harold J. Kushner) - Semantic Scholar

Abedi F, Abu Hassan M, Arifin MN: Lyapunov function for nonuniform in time global asymptotic stability in probability with application to feedback stabilization. Acta Appl.

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IMA J. Control Inf. Automatica , IEEE Trans. Imprint: Academic Press.

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Institutional Subscription. Free Shipping Free global shipping No minimum order. The previous stability criteria are extended to give the delay-dependent stabilization conditions in terms of LMIs. Furthermore, an LMI optimization algorithm is proposed to find the maximum allowable delay of the system.

Stochastic Control # 4 Dr. S. Meyn

Finally, numerical examples show that the proposed results are effective and much less conservative than some existing results. Sign In or Create an Account. Sign In. Advanced Search. Article Navigation.

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