Asymptotic stability in probability of singular stochastic systems with Markovian switchings

Ding, Yucai; Zhong, Shouming; Long, Siyu

doi:10.1002/rnc.3795

Cited by 29 publications

(6 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Switched systems as a special class of hybrid dynamical systems for which the system dynamics are comprised of a countable family of subsystems. Investigation on analyzing stability of switched systems in control system analysis has attracted a considerable research attention, [24][25][26][27][28][29][30][31] which have been applied in wide realistic fields, for instance, synchronization, [32][33][34] multiagent systems, [35][36][37] and chemical engineering, 38 etc. Amongst the problem of stability analysis, the estimate of domain of attraction is one of the most interesting and serious challenges for switched systems.…”

Section: Introductionmentioning

confidence: 99%

Computing multiple Lyapunov‐like functions for inner estimates of domains of attraction of switched hybrid systems

Zheng

She

et al. 2018

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

Summary Domain of attraction plays an important role in stability analysis and safety verification of nonlinear control systems. In this paper, based on the concept of multiple Lyapunov‐like functions, we propose iteration algorithms for computing inner estimates of domains of attraction for a class of switched hybrid systems, where the state space is composed of several regions and each region is described by polyhedral sets. Starting with an initial inner estimate of domain of attraction, we firstly present a theoretical framework for obtaining a larger inner estimate by iteratively computing multiple Lyapunov‐like functions. Successively, the theoretical framework is underapproximatively realized by using S‐procedure and sums of squares programming, associated with the coordinatewise iteration method. Afterwards, for obtaining a required initial inner estimate of domain of attraction, we propose an alternative higher‐order truncation and linear semidefinite programming based method for computing a common Lyapunov function. Especially, a bisection method based improvement is proposed for obtaining better estimates in each iteration step. Finally, we implement proposed algorithms and test them on numerical examples with comparisons. These computation and comparison results show that the advantages of our multiple Lyapunov‐like functions based algorithm. Especially, we provide alternative underapproximations for avoiding the possible numerical problem.

show abstract

Section: Introductionmentioning

confidence: 99%

Computing multiple Lyapunov‐like functions for inner estimates of domains of attraction of switched hybrid systems

Zheng

She

et al. 2018

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

“…Besides, recall that the Markov model simulates well some stochastic problems in real engineering [26][27][28][29][30][31]. In Model 7, k i (i = 1, 2, 3) represents the feedback profit coefficient, which is also stochastic in a dynamic economic market.…”

Section: Remarkmentioning

confidence: 99%

Global Stability of a Markovian Jumping Chaotic Financial System with Partially Unknown Transition Rates under Impulsive Control Involved in the Positive Interest Rate

Rao

2019

Mathematics

View full text Add to dashboard Cite

The intrinsic instability of the financial system itself results in chaos and unpredictable economic behavior. To gain the globally asymptotic stability of the equilibrium point with a positive interest rate of the chaotic financial system, pulse control is sometimes very necessary and is employed in this paper to derive the globally exponential stability of financial system. It should be pointed out that the delayed feedback model brings an essential difficulty so that the regional control method has to be adopted. In this paper, the author firstly employs impulsive control, regional control, the Lyapunov function technique, and variational methods to derive the stochastically globally asymptotic stability criterion of the economic balance point with a positive interest rate for a delayed feedback financial system with Markovian jumping and partially unknown transition rates. Besides, the mathematical induction method and the proof by contradiction are applied synthetically to deduce the globally exponential stability of the equilibrium point with a positive interest rate for the impulsive financial system without time-delays. Moreover, numerical examples illustrate that under suitable data conditions on the two main criteria mentioned above, the interest rates are positive decimals when the financial system reaches stability, which means better economic significance.

show abstract

“…When singular systems experience abrupt changes in their structures, it is natural to model them as singular Markovian jump systems [1,2]. The analysis and synthesis of such class of systems have gained considerable attention because of their importance in applications (see, e.g., the literature [3][4][5][6][7][8][9][10] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Estimation and Synthesis of Reachable Set for Singular Markovian Jump Systems

Ding

Liu

2018

Complexity

Self Cite

View full text Add to dashboard Cite

The problems of reachable set estimation and state-feedback controller design are investigated for singular Markovian jump systems with bounded input disturbances. Based on the Lyapunov approach, several new sufficient conditions on state reachable set and output reachable set are derived to ensure the existence of ellipsoids that bound the system states and output, respectively. Moreover, a state-feedback controller is also designed based on the estimated reachable set. The derived sufficient conditions are expressed in terms of linear matrix inequalities. The effectiveness of the proposed results is illustrated by numerical examples.

show abstract

Asymptotic stability in probability of singular stochastic systems with Markovian switchings

Cited by 29 publications

References 34 publications

Computing multiple Lyapunov‐like functions for inner estimates of domains of attraction of switched hybrid systems

Computing multiple Lyapunov‐like functions for inner estimates of domains of attraction of switched hybrid systems

Global Stability of a Markovian Jumping Chaotic Financial System with Partially Unknown Transition Rates under Impulsive Control Involved in the Positive Interest Rate

Estimation and Synthesis of Reachable Set for Singular Markovian Jump Systems

Contact Info

Product

Resources

About