A Sufficient Condition for the Stability of Discrete-Time Systems With State-Dependent Coefficient Matrices

Yuno, Tsuyoshi; Ohtsuka, Toshiyuki

doi:10.1109/tac.2013.2270318

Cited by 4 publications

(3 citation statements)

References 7 publications

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“…Assume the delays 1 (k) = 3 + sin(k) ∈ [2, 4) and 2 (k) = 5 + sin(k) ∈ [4,6] take values in random sense that follow uniform distribution in the corresponding intervals. In general, the probabilities of the stochastic variables (k) and i (k), i = 1, 2, 3 can be achieved early through statistical tests.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…[1][2][3][4][5] In particular, when implementing the delayed continuous-time systems for computer simulation, it becomes essential to formulate discrete-time system that is an analogue of the continuous-time delayed systems. So in recent years, the researchers eventually paid attention for investigation on discrete-time systems, for details see previous studies [6][7][8][9][10] and references therein. In practice, discrete-time systems have found many applications, such as hydraulic, rolling mill systems, automatic control, secure communication, signal and image processing, chemical processes, and long transmission lines in pneumatic.…”

Section: Introductionmentioning

confidence: 99%

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Robust guaranteed cost state estimation for discrete‐time systems with random delays and random uncertainties

Nishanthi

Banu

Balasubramaniam

2017

Adaptive Control & Signal

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This paper investigates the guaranteed cost state estimation problem for a class of discrete-time systems based on the Wirtinger-based inequality with randomly occurring delays (RODs) and randomly occurring uncertainties (ROUs). The time-varying delays and parameter uncertainties are considered to occur in random way. Certain mutually uncorrelated Bernoulli-distributed white-noise sequences are included to govern the random occurrences. The cost function is chosen appropriately to guarantee an adequate level of performance. New sufficient conditions are established in terms of linear matrix inequalities to ensure the estimation of state vectors for the given discrete-time system by constructing Lyapunov-Krasovskii functionals and using reciprocally convex lemma. The advantage of using the proposed results is illustrated via numerical examples.

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Section: Numerical Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust guaranteed cost state estimation for discrete‐time systems with random delays and random uncertainties

Nishanthi

Banu

Balasubramaniam

2017

Adaptive Control & Signal

View full text Add to dashboard Cite

show abstract

“…The researches of switched systems are more challenging than nonswitched systems on account of their abundant and diverse switching rules 5 . The common switching mechanisms can be classified into state‐dependent switching rule, 6 time‐dependent switching rule, average dwell‐time switching rule, 7,8 and random switching rule 9,10 . As mentioned in Reference 11, the switched systems with stable subsystems maybe unstable due to improper switching rules; and the switched systems with unstable subsystems can be stable by choosing proper switching rules.…”

Section: Introductionmentioning

confidence: 99%

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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Guaranteed Cost Sliding Mode Control of Switched Systems with Known Sojourn Probabilities

Zhao

Niu

2018

Int. J. Control Autom. Syst.

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A Sufficient Condition for the Stability of Discrete-Time Systems With State-Dependent Coefficient Matrices

Cited by 4 publications

References 7 publications

Robust guaranteed cost state estimation for discrete‐time systems with random delays and random uncertainties

Robust guaranteed cost state estimation for discrete‐time systems with random delays and random uncertainties

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

Guaranteed Cost Sliding Mode Control of Switched Systems with Known Sojourn Probabilities

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