# Event triggered control of two time scale system

##### Citations

77 citations

38 citations

### Cites background from "Event triggered control of two time..."

...In [12] ETC of a linear TTSS is studied....

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...In place of using full state information to determine the triggering instances (such as in [3]–[5] and [12] etc....

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2 citations

### Cites background from "Event triggered control of two time..."

...where the matrix A22 is supposed to be invertible and the same assumption was used in Bhandari et al. (2018). Based on the expressions ofH andL in (8), the dynamics of the states (ξT , ηT)T can be written as ( ξ̇...

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...In Bhandari, Fulwani, and Gupta (2017) and Bhandari, Fulwani, and Gupta (2018), the event-triggered control of both the slow and fast dynamics was implemented for linear systems, where the event-triggering condition utilised a time-varying threshold....

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1 citations

### Cites background from "Event triggered control of two time..."

...Asynchronous sampling provides key points of interest over time-triggered sampling in terms of network utilization and communication load [14]....

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### Cites background or result from "Event triggered control of two time..."

...Model-Based Event Triggered Control In the majority of event-triggered control systems in the literature, the controller is a typical sampled data controller which generates a piece-wise constant input by keeping the received measurements constant till the arrival of new measurements at the next sampling instant [3], [16]....

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...Proof: This proof is in line with [16]....

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...In a recent work [16] ETC of linear SPS is discussed....

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##### References

16 citations

### "Event triggered control of two time..." refers background or methods in this paper

...0 0 0 1 u (29) Here n = 2 and m = 2 and control is designed using composite control technique defined in [6] as u = ( −1 −0.86 ) x1 + ( −0.18 −0.05 ) x2 (30) So that both Λ0 and Λ22 are Hurwitz....

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...As Λ22 is Hurwitz, hence it is non singular, and (9) is in standard singularly perturbed form....

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...The following controller is designed u(t) = K1x1(t)+K2x2(t) (5) so as to ensure satisfactory closed loop response, where K = [K1,K2] is such that both slow manifold Λ0 =(A11+B1K1)− (A12 +B1K2)(A22 +B2K2) −1(A21 +B2K1) and fast manifold (A22 +B2K2) of closed loop system (4) are Hurwitz stable....

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...Slow subsystem is given as ẋs(t) = A0.xs(t), (2) where xs(0) = x 0 1 and A0 = A11 −A12A −1 22 A21, and the fast subsystem with τ = ( tε ) dx f (τ) dτ = A22x f (τ) (3) where x f (0) = x 0 2 +A −1 22 A21x 0 1 Lemma 1: If P is a Hurwitz matrix and P0 is a constant matrix then there exists a sufficiently small λ such that (P+λ P0) is also a Hurwitz matrix....

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...Lemma 1 is about a property of Hurwitz matrix which says that small bounded perturbation of Hurwitz matrix is also Hurwitz [9]....

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8 citations

### "Event triggered control of two time..." refers background in this paper

...Similarly [10] deals with two-timescale system (TTSS) and a derives a necessary data rate for feedback channel independent of the small parameter so that the plant is stable....

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