Observer-based dissipative control for Markovian jump systems via delta operators

Sakthivel, R.; Rathika, M.; Santra, Srimanta; Malik, Muslim

doi:10.1080/00207721.2016.1177131

Cited by 26 publications

(7 citation statements)

References 33 publications

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“…Therefore, it is necessary to develop the research about Markovian jumping systems with uncertain transition rates. () Sakthivel et al considered an observer‐based dissipative control for Markovian jump systems via delta operators. The authors considered a problem of robust sampled‐data control for uncertain switched neutral systems with probabilistic input delay.…”

Section: Introductionmentioning

confidence: 99%

Exponential stability of switched Markovian jumping neutral‐type systems with generally incomplete transition rates

Kao

Yang

Park

2017

Intl J Robust & Nonlinear

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In this paper, the exponential mean-square stability of neutral switching Markovian jump systems with generally incomplete transition probabilities is investigated. The model discussed in this paper concludes both deterministic switching signals and Markovian jumping signals. The transition rates of the jumping process are assumed to be partly available, that is, some elements have been exactly known, some have been merely known with lower and upper bounds, and others may have no information to use. Based on the Lyapunov-Krasovskii functional method, sufficient conditions on the exponential mean-square stability of the considered system are derived in terms of liner matrix inequalities. A numerical example is provided to show the feasibility and effectiveness of the proposed results.KEYWORDS exponential mean-square stability, generally uncertain transition rates, neutral-type Markovian jumping systems INTRODUCTIONNeutral-type systems play an important role in many branches of natural science and engineering science 1-3 because many practical delay systems could be modeled by neutral-type systems. The differential expression of a neutral-type system concludes not only the derivative term of the current state but also the derivative of the past state. 4,5 Many scholars have deeply investigated the stability and control problem of neutral-type systems, 6-9 including approximate controllability, 10 observer-based control, 11,12  ∞ control, 13-15 and reliable control. 16,17 Arino and Nosov 18 studied the stability and asymptotic properties of a class of neutral-type functional differential equations based on the pattern equation method.Int J Robust Nonlinear Control. 2018;28:1583-1596.wileyonlinelibrary.com/journal/rnc

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Section: Introductionmentioning

confidence: 99%

Exponential stability of switched Markovian jumping neutral‐type systems with generally incomplete transition rates

Kao

Yang

Park

2017

Intl J Robust & Nonlinear

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“…It is worth noting that the present investigation only focuses on the H ∞ robust control problems for a class of singular stochastic hybrid systems with Markovian jump in the sense of mean square, and so it would be quite naturally to deal with the issue of H ∞ performance in different kinds of convergence form the view of stochastic dynamical systems, including in probability 42 and in distribution. 43 In addition, it should be believed that the idea and approach developed in this paper could provide valuable insight into the modeling, analysis, and control of many large-scale complex networked singular systems with Markovian jump form practical engineering perspective, such as communication networks, neural networks, genetic regulatory networks, and power-grid networks, which will be an interesting and challenging issue in future research in this direction.…”

Section: Resultsmentioning

confidence: 99%

H_∞ robust control based on event‐triggered sampling for hybrid systems with singular Markovian jump

Pan

Zhou

2018

Math Methods in App Sciences

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The problem of H ∞ robust control based on event-triggered sampling for a class of singular hybrid systems with Markovian jump is considered in this paper. The primary object of this paper here is to design the event-triggered sampling controller for a class of uncertain singular Markovian systems, and two fundamental issues on mean square exponential admissibility and H ∞ robust performance are fully addressed. By making use of a suitable Lyapunov functional, in combination with both infinitesimal operator and linear matrices inequalities(LMIs), the sufficient criteria are derived to guarantee the controlled singular hybrid system with Markovian jump is robustly exponentially mean-square admissible and has a prescribed H ∞ performance . Finally, a typical RLC circuit system is given to show the effectiveness of the proposed control method. KEYWORDS descriptor systems, event-triggered, linear matrix inequalities (LMIs), Markovian jump, stochastic control 790

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“…This method is very common to solve such problem. Nevertheless, as in [42], the cone complementarity approach is adopted in this work as a second alternative. • To synthesise the observer and controller gains, the SVD [31, 32, 43], the pseudo inverse of the output matrix [33], and the Finsler's lemma with a particular structure of some decision matrices [44] have been used. However, these techniques are difficult to apply when the disturbance affects the measurements.…”

Section: Dissipative Observer‐based Control Synthesismentioning

confidence: 99%

Robust dissipative observer‐based control design for discrete‐time switched systems with time‐varying delay

Regaieg

Kchaou

Bosche

et al. 2019

IET Control Theory & Applications

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Observer-based dissipative control for Markovian jump systems via delta operators

Cited by 26 publications

References 33 publications

Exponential stability of switched Markovian jumping neutral‐type systems with generally incomplete transition rates

Exponential stability of switched Markovian jumping neutral‐type systems with generally incomplete transition rates

H_∞ robust control based on event‐triggered sampling for hybrid systems with singular Markovian jump

Robust dissipative observer‐based control design for discrete‐time switched systems with time‐varying delay

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Observer-based dissipative control for Markovian jump systems via delta operators

Cited by 26 publications

References 33 publications

Exponential stability of switched Markovian jumping neutral‐type systems with generally incomplete transition rates

Exponential stability of switched Markovian jumping neutral‐type systems with generally incomplete transition rates

H∞ robust control based on event‐triggered sampling for hybrid systems with singular Markovian jump

Robust dissipative observer‐based control design for discrete‐time switched systems with time‐varying delay

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H_∞ robust control based on event‐triggered sampling for hybrid systems with singular Markovian jump