Stochastic stability of systems with semi-Markovian switching

Schiøler, Henrik; Simonsen, Maria; Leth, John

doi:10.1016/j.automatica.2014.09.008

Cited by 66 publications

(29 citation statements)

References 11 publications

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“…Under this assumption, the stability and stabilization problems were investigated in [12,14] for systems with discrete-time semi-Markovian switching by using the semi-Markovian kernel approach. However, for continuous-time semi-Markovian switching, some special assumptions should be given for semiMarkovian process in [6,[9][10][11]. For example, the distribution F ij (t) only depends on i in [6,[9][10][11], and satisfies the Phasetype distribution in [10,11].…”

Section: A Stability Of System With Semi-markovian Switchingmentioning

confidence: 99%

“…However, the moment stability presented in [8,9] can not imply the GAS a. s. and almost surely exponentially stable (ES a. s.), which was also pointed out in [8], and the method provided in [8,9] cannot be directly applied to the investigation on GAS a. s. and ES a. s. Thus, it is still open to address the GAS a. s. and ES a. s. for the system with Markovian/semi-Markovian switching by using the stationary distribution of Markov chains/embedded Markov chain. In addition, the sojourn time for switching signals were assumed to satisfy an exponential or a uniform distribution in [6], which are the special cases of renewal process.…”

Section: Introductionmentioning

confidence: 99%

“…Subsequently, the multiple Lyapunov-like function method has been widely applied to the study on the stability of randomly switched systems [6][7][8][9]. A system with Markovian switching is an important randomly switched system, its active time for each subsystem satisfies the exponential distribution, which has limited the applications of Markovian switching.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, by using the comparison theorem and the stationary distribution of Markov chains, the moment stability was studied for the system with Markovian switching in [8]. In [9], the comparison method introduced in [8] was generalized to investigate the moment stability for systems with semi-Markovian switching.…”

Section: Introductionmentioning

confidence: 99%

“…A system with Markovian switching is an important randomly switched system, its active time for each subsystem satisfies the exponential distribution, which has limited the applications of Markovian switching. To overcome this restriction, the stability of the system with semi-Markovian switching has been investigated in [6,[9][10][11][12][13][14], where the semi-Markovian switching does not necessarily satisfy memoryless property of Markov switching. In [12], the stability and stabilization were considered for switched systems with discrete-time semi-Markovian signals by using the semi-Markovian kernel approach.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Stability Analysis for Continuous-Time Switched Systems With Stochastic Switching Signals

Tang

Cao

et al. 2018

IEEE Trans. Automat. Contr.

157

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Abstract-This paper is concerned with the stability problem of randomly switched systems. By using the probability analysis method, the almost surely globally asymptotical stability and almost surely exponential stability are investigated for switched systems with semi-Markovian switching, Markovian switching and renewal process switching signals, respectively. Two examples are presented to demonstrate the effectiveness of the proposed results, in which an example of consensus of multi-agent systems with nonlinear dynamics is taken into account.

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Section: A Stability Of System With Semi-markovian Switchingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Stability Analysis for Continuous-Time Switched Systems With Stochastic Switching Signals

Tang

Cao

et al. 2018

IEEE Trans. Automat. Contr.

157

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Stochastic sliding mode control of active vehicle suspension with mismatched uncertainty and multiplicative perturbations

Moghadam

Kebriaei

2019

Asian Journal of Control

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The purpose of this paper is to investigate the stochastic sliding mode controller design for uncertain model of vehicle suspension. The Itô stochastic model of quarter-car is considered applying both parametric stochastic perturbations and mismatched uncertainty of road disturbance. To tackle with uncertainties of model a non-semi-martingale stochastic sliding dynamic is obtained employing a proportional-integral switching surface. By means of linear matrix inequalities (LMIs) and stochastic extension of Lyapunov method, a sufficient condition is derived to guarantee the mean-square stability of the stochastic dynamics in the specified switching surface for all admissible mismatched uncertainties. Furthermore, the synthesized sliding mode controller guarantees the reachability of the determined sliding surface. A simulation study is performed to evaluate the effectiveness of stochastic sliding mode control approach.

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Non‐fragile reliable control of nonlinear positive semi‐Markovian jump systems with nonlinear actuator faults

Liu

Song

et al. 2022

Asian Journal of Control

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This paper investigates the non‐fragile reliable control of nonlinear positive semi‐Markovian jump systems with nonlinear actuator faults. First, a novel fault model consisting of linear and nonlinear terms is established for the systems. By constructing a stochastic co‐positive Lyapunov function, the non‐fragile reliable controller is designed for the systems with additive gain perturbations using matrix decomposition technique. Then, the proposed design is extended for dealing with multiplicative gain perturbations and variable gain perturbations. Under the designed controllers, the resulting closed‐loop systems are positive and stochastically stable. All presented conditions are solvable in terms of linear programming. Finally, two illustrative examples are provided to verify the effectiveness of the theoretical results.

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Stochastic stability of systems with semi-Markovian switching

Cited by 66 publications

References 11 publications

Stability Analysis for Continuous-Time Switched Systems With Stochastic Switching Signals

Stability Analysis for Continuous-Time Switched Systems With Stochastic Switching Signals

Stochastic sliding mode control of active vehicle suspension with mismatched uncertainty and multiplicative perturbations

Non‐fragile reliable control of nonlinear positive semi‐Markovian jump systems with nonlinear actuator faults

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