Stabilization of saturated discrete-time fuzzy systems

Benzaouia, Abdellah; Gounane, Said; Tadeo, Fernando

doi:10.1007/s12555-011-0319-8

Cited by 9 publications

(10 citation statements)

References 23 publications

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“…Example Consider a truck‐trailer model given as follows:

({, \begin{matrix} right & left x_{1} (k + 1) = (1 - \frac{v t}{L}) x_{1} (k) + \frac{v t}{L} ν (k) & right \\ right & left x_{2} (k + 1) = (\frac{v t}{L}) x_{1} (k) + x_{2} (k) + 0.2 w (k) \\ right & left x_{3} (k + 1) = x_{3} (k) + v t s i n (θ_{k}) + 0.1 w (k) \\ right & left z (k) = C_{1} x ((k) + \frac{v t}{L} ν (k) \\ right & left y (k) = C_{2} x ((k) \end{matrix})

θ_{k} = ((), \frac{v t}{2 L}) x_{1} ((), k) + x_{2} ((), k)

The nonlinear system is represented by the following uncertain T‐S fuzzy model:

\begin{matrix} Plant rule 1 : if θ_{k} is α_{1} then: \\ x ((), k + 1) = ((), A_{1} + M_{1} normalΘ ((), k) N_{1} ...) \end{matrix}

…”

Section: Applicationmentioning

confidence: 99%

“…In order to make some comparisons, we consider the results issued from and . The output feedback control gains of SOF without actuators saturation proposed in is:

K_{1} = 0.1430, K_{2} = 0.1530

The state feedback control gains of PDC with actuators saturation proposed in is:

K_{1} = K_{2} = ([], \begin{matrix} centerarray \\ array 2.40552 & array - 1.3751 & array 0.1456 \end{matrix})

The state feedback control gains of PDC with constrained proposed in is:

\begin{matrix} right & left K_{1} = [\begin{array}{c} 1.8985 & - 2.0338 & 0.2439 \end{array}], & right \\ right & left K_{2} = [\begin{array}{c} 1.8985 & - 1.7002 & 0.3022 \end{array}] \end{matrix}

Now, solving the optimization problem of Theorems 3 and 4 for saturation level

ū = 1, γ = 0.5

and λ = 2, we obtain the results given in Table .…”

Section: Applicationmentioning

confidence: 99%

“…In order to illustrate the effectiveness of the proposed design methods, we propose a comparison with the results based on PDC saturated control via quadratic Lyapunov functions . Figures and show four simulation results: the SOF saturated control (in blue), SOF without actuators saturation (in red) and the PDC saturated control (in green) and constrained control (in black) . The initial conditions for this example are

x_{01} = ([], 0.7 0 0)

:…”

Section: Applicationmentioning

confidence: 99%

“…Fuzzy sets 1 is around k and 2 for k around ± (179.99Π∕180) , 1 = sin( k ) k , 2 = 1 − 1 . In order to make some comparisons, we consider the results issued from [18,42,32] and [33]. The output feedback control gains of SOF without actuators saturation proposed in [18] is:…”

Section: Examplementioning

confidence: 99%

“…Therefore, the control system design must take into account these input constraints in order not to degrade the performance of the closed-loop system that can even lead to instability issues [8,10,25,26,[30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45]. Many results are reported in the literature regarding stability analysis of linear (more recently, see [35][36][37][38]) and nonlinear systems [8,10,16,25,26,[31][32][33][34][40][41][42]45] subject to input constraints. Several approaches were experienced with T-S systems: bound on the initial conditions to avoid the input saturation in low gain control laws [16,26,40]; estimation of the attraction domain in the presence of actuator saturation [8,10,16,38,40,41,…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Robust H_∞ static output‐feedback control for discrete‐time fuzzy systems with actuator saturation via fuzzy Lyapunov functions

Saifia

Chadli

Labiod

et al. 2019

Asian Journal of Control

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In this paper, we present a new scheme for designing a H∞ stabilizing controller for discrete‐time Takagi‐Sugeno fuzzy systems with actuator saturation and external disturbances. The weighting‐dependent Lyapunov functions approach is used to design a robust static output‐feedback controller. To address the input saturation problem, both constrained and saturated control input cases are considered. In both cases, stabilization conditions of the fuzzy system are formulated as a convex optimization problem in terms of linear matrix inequalities. Two simulation examples are included to illustrate the effectiveness of the proposed design methods. A comparison with the results given in recent literature on the subject is also presented.

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“…Example Consider a truck‐trailer model given as follows:

({, \begin{matrix} right & left x_{1} (k + 1) = (1 - \frac{v t}{L}) x_{1} (k) + \frac{v t}{L} ν (k) & right \\ right & left x_{2} (k + 1) = (\frac{v t}{L}) x_{1} (k) + x_{2} (k) + 0.2 w (k) \\ right & left x_{3} (k + 1) = x_{3} (k) + v t s i n (θ_{k}) + 0.1 w (k) \\ right & left z (k) = C_{1} x ((k) + \frac{v t}{L} ν (k) \\ right & left y (k) = C_{2} x ((k) \end{matrix})

θ_{k} = ((), \frac{v t}{2 L}) x_{1} ((), k) + x_{2} ((), k)

The nonlinear system is represented by the following uncertain T‐S fuzzy model:

\begin{matrix} Plant rule 1 : if θ_{k} is α_{1} then: \\ x ((), k + 1) = ((), A_{1} + M_{1} normalΘ ((), k) N_{1} ...) \end{matrix}

…”

Section: Applicationmentioning

confidence: 99%

“…In order to make some comparisons, we consider the results issued from and . The output feedback control gains of SOF without actuators saturation proposed in is: