Analysis and synthesis of randomly switched systems with known sojourn probabilities

Tian, Engang; Yue, Dong; Yang, Tingting

doi:10.1016/j.ins.2014.02.129

Cited by 22 publications

(11 citation statements)

References 41 publications

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“…In order to obtain the required results, we assume that the following conditions hold. 15,27 Assumption 1. The probability of a switched system staying in a particular subsystem is assumed to be known a priori, ie,…”

Section: Problem Formulationmentioning

confidence: 99%

“…However, there are only a few number of publications in the existing literature that are based on sojourn probabilities and linear matrix inequality (LMI) techniques. Tian et al 15 obtained a stabilizing controller design for randomly switched linear discrete-time systems based on sojourn probabilities, and it was assumed that these probabilities are known a priori. In the work of Banu and Balasubramaniam, 16 a new set of delay-dependent sufficient conditions was obtained for the stability and stabilization of a class of discrete-time switched fuzzy systems with known sojourn probabilities by using the Lyapunov functional technique.…”

Section: Introductionmentioning

confidence: 99%

“…Proof. The proof of this theorem can be obtained by considering the Lyapunov function as in Equation 15 and following similar steps in Theorem 1.…”

Section: Moreover By Introducing the Virtual Input And Output Vectorsmentioning

confidence: 99%

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Fault estimation and tolerant control for discrete‐time switched systems with sojourn probabilities

Sakthivel

Joby

Santra

et al. 2017

Adaptive Control & Signal

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This paper addresses the issue of fault estimation and accommodation for a discrete-time switched system with actuator faults. Here, we assume that the sojourn probabilities are known a priori. By using the reduced-order observer method, the sojourn probability approach, and the Lyapunov technique, a fault estimation algorithm is obtained for the considered system. The main objective of this work is to design a dynamic output feedback fault-tolerant controller based on the obtained fault estimation information such that the closed-loop discrete-time switched system with available sojourn probabilities is robustly mean-square stable and satisfies a prescribed mixed H ∞ and passivity disturbance attenuation level in the presence of actuator faults. More precisely, a dynamic output feedback fault-tolerant controller is established in terms of linear matrix inequalities. Finally, numerical examples are provided to illustrate the usefulness and effectiveness of the proposed design technique.

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Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fault estimation and tolerant control for discrete‐time switched systems with sojourn probabilities

Sakthivel

Joby

Santra

et al. 2017

Adaptive Control & Signal

View full text Add to dashboard Cite

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“…A general discrete‐time switched system can be characterized by the difference equation x ( k + 1) = A r ( k ) x ( k ), where

x (k) \in {double-struckR}^{n}

is the state, A r ( k ) are functions of the switching signals, piecewise‐constant function

r (k) : Z^{+} \to scriptS

is called a switching signal, and r ( k ) = i means that the i th subsystem is activated at a certain discrete‐time instant. An effective and alternative rule for switching in the stochastic switched systems known as Known Sojourn Probability (KSP) that can be calculated from the history of the system has been proposed in recent years as in . The main advantage of this KSP information is that it can be measured easily than that of the transition probabilities.…”

Section: Introductionmentioning

confidence: 99%

“…S is called a switching signal, and r.k/ D i means that the ith subsystem is activated at a certain discrete-time instant. An effective and alternative rule for switching in the stochastic switched systems known as Known Sojourn Probability (KSP) that can be calculated from the history of the system has been proposed in recent years as in [16,17]. The main advantage of this KSP information is that it can be measured easily than that of the transition probabilities.…”

Section: Introductionmentioning

confidence: 99%

Combined and passivity control for networked control systems with random gain fluctuations and sojourn probabilities: A switched system approach

Sasirekha

Rakkiyappan

Cao

2017

Intl J Robust & Nonlinear

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Summary On the basis of the passivity theory, the problem of designing non‐fragile H∞ control for a class of networked control systems (NCSs) with the plant being a switched system is presented. The NCSs under consideration are modeled by considering the network‐induced imperfections like transmission delays and packet dropouts as a single time‐varying delay. The network status is assumed to vary on the basis of sojourn probabilities, and these probabilities are known a prior. The controller is designed including stochastic fluctuations in its gain matrix by considering the Bernoulli distributed white sequence along with time‐varying probability measures. The key steps in this method are to construct an improved Lyapunov–Krasovskii Functional and to utilize reciprocally convex technique. The sojourn probability‐dependent sufficient criteria are obtained to ensure the closed‐loop, mode‐dependent switched NCSs to be robustly stochastically stable on the basis of the combined H∞ and passivity performance. The effectiveness of the proposed method is illustrated through an example. Copyright © 2017 John Wiley & Sons, Ltd.

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Protocol‐based collaborative design for discrete‐time switched systems with sojourn probabilities

Zhu

Wei

et al. 2020

Intl J Robust & Nonlinear

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This article focuses on the collaborative design of a class of discrete-time switched systems with sojourn probabilities. For the purpose of preventing the data collision, the Try-Once-Discard (TOD) protocol is employed to govern the information transmission between sensors and the controller. Moreover, it is worth noting that the values of sojourn probabilities, which are not given ahead, have an effect on the system stability. As a consequence, a novel collaborative design framework is established, in which the sojourn probability and static output-feedback controller are to be designed simultaneously. By considering the effect from the TOD protocol and using the Lyapunov function related to the mode and protocol, a sufficient condition is derived to guarantee the exponential mean square stability of the closed-loop system with a prescribed lower bound on the decay rate. Then, the desired sojourn probabilities and controller gains dependent on the corresponding mode and protocol are obtained in terms of convex optimization method with equality constraints. Subsequently, an estimation approach is provided to estimate the decay rate and decay coefficient of the closed-loop system. Finally, one numerical example is given to testify the effectiveness of the proposed design approach.

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Analysis and synthesis of randomly switched systems with known sojourn probabilities

Cited by 22 publications

References 41 publications

Fault estimation and tolerant control for discrete‐time switched systems with sojourn probabilities

Fault estimation and tolerant control for discrete‐time switched systems with sojourn probabilities

Combined and passivity control for networked control systems with random gain fluctuations and sojourn probabilities: A switched system approach

Protocol‐based collaborative design for discrete‐time switched systems with sojourn probabilities

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