Sliding mode control for semi-Markovian jump systems via output feedback
Citations
199 citations
Cites background from "Sliding mode control for semi-Marko..."
...Furthermore, without taking the singularity into account, singular S-MJSs can be translated into nonsingular S-MJSs [21]–[23]....
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...Remark 6: For the first question (Q1), different from nonsingular S-MJSs [21]–[23], we need to derive the weak infinitesimal operator from the point of view of probability distribution under the influence of singular factor (see formulas (17)-(20))....
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...Therefore, the following three essential difficulties during the problem of OBASMC for nonlinear uncertain singular S-MJSs should be solved: Q1: Compared with nonsingular S-MJSs [21]–[23], how to derive the weak infinitesimal operator under the influence of singular factor? Q2: The controller gain matrices Ki in [9] cannot be solved directly....
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...Second, the S-MJSs considered in [21]–[23] were nonsingular while the model in this paper is singular....
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191 citations
Additional excerpts
..., N2} with the following probability transition [31]: Pr{rt+ δ = j|rt = i, gt = α} = { π ij (h)δ + o(δ), i = j 1 + π ii (h)δ + o(δ), i = j where δ > 0 and limh→0 o(δ)/δ = 0, π ij (h) > 0(i = j) is the TR from mode i at time t to mode j at time t+ δ, and π ii (h) = −Σj = i π ij (h) < 0 for each i ∈ S2 , here, h represents the sojourn time....
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191 citations
135 citations
Cites background or methods from "Sliding mode control for semi-Marko..."
...Therefore, some remarkable works about sliding mode control for MJSs and S-MJSs have attracted considerable attention [3], [7], [8], [10], [15]–[17], [22]–[24]....
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...Fourth, the S-MJSs considered in [6]–[8] are nonsingular, whereas the model in this paper is singular....
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...Remark 5: For the first question (Q1), different from S-MJSs without stochastic disturbance [5]–[12] and nonsingular S-MJSs [6]–[8], we need to derive the weak infinitesimal operator from the viewpoints of probability distribution by the use of Itô’s formula and Euler– Maruyama formula under the influences of singular factor and stochastic factor (see formulas (25)–(32) for some details)....
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...Remark 4: Compared with nonsingular S-MJSs [6]–[8], there are some difficulties in considering singular property....
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...Q1: Compared with S-MJSs [5]–[12] without stochastic disturbance and nonsingular S-MJSs [6]–[8], how to derive the weak infinitesimal operator under the influences of stochastic disturbance and singular factor? Q2: How to design the sliding mode control law so as to guarantee that the state responses of dynamic system can be driven onto the predefined sliding switching surfaces in finite time under the semiMarkov switching? The above aspects stimulate our research interests....
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130 citations
Cites background from "Sliding mode control for semi-Marko..."
...Remark 6: As mentioned in [19], we have λ̄ij = ∫∞ 0 λ̄ij (h)fi(h)dh, where fi(h) is the probability distribution function of the ST h staying at mode i, which means that the range of the ST h is from 0 to ∞....
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...It is noted that S-MJSs have gained particular research interests, such as stability [14]–[17], sliding mode control [18], [19], and quantized control [20]....
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References
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