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This paper proposes a new hierarchical identification method for fractional-order systems. In this method, a SISO (single input, single output) state space model has been considered in which parameters and also state variables should be estimated.  By using a linear transformation and a shift operator, the system will be transformed into a form appropriate for identification of a fractional-order system. Then, the unknown parameters will be identified through a recursive least squares method and the states will be estimated using a fractional order Kalman filter. This identification method is based on the hierarchical identification principle that reduces the computational burden and is easy to implement on computer. The promising performance of the proposed method is verified using two stable fractional-order systems.    

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This paper studies the consensus problem of nonlinear leader-following multi-agent systems (MAS). To do this, the error dynamics between the leader agent and follower ones are described via a Takagi-Sugeno (TS) fuzzy model. If the obtained TS fuzzy model is stable, then all of the nonlinear agents reach consensus. The consensus problem is investigated based on the parameterized or fuzzy Lyapunov function combined with a technique of introducing slack matrices. The slack matrices cause to decouple the Lyapunov matrices from systems ones and therefore, sufficient consensus conditions are obtained in terms of linear matrix inequalities (LMIs). The proposed slack matrices add an extra degree-of-freedom to the LMI conditions and also decrease the conservativeness of the LMI-based conditions. Finally, in order to illustrate the effectiveness and merits of the proposed method, a numerical example for the consensus problem of nonlinear leader-follower MAS with thirteen followers is solved.

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In this paper, the stability problem of nonlinear first order hyperbolic partial differential equations (PDE) systems is investigated. Based on Lyapunov stability theorem, the sufficient conditions to guarantee the stability of Takagi-Sugeno (TS) fuzzy hyperbolic PDE model are achieved in terms of spatially varying linear matrix inequalities (SVLMI). To investigate the exponentially stabilization of nonlinear first order hyperbolic PDE systems, a fuzzy Lyapunov function is considered. Then, some new space varying slack matrices are introduced to conduct the stability analysis. The proposed stability conditions are more relaxed than the newly published one. Furthermore, the problem of applying some constraints on control input is studied through this paper. Hence, the performance of the controller is improved in the proposed approach. Finally, in order to evaluate the validity of the proposed approach, a practical application of nonisothermal plug flow reactor (PFR) is considered.  

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Stress urinary incontinence (SUI) is characterized by the involuntary transurethral leakage of urine caused by an increase in abdominal pressure in the lack of an adequate bladder‎ ‎contraction that raises the vesical pressure to a level that exceeds urethral pressure‎. ‎Adult women are most commonly affected by SUI which is believed to be caused in part by‎ ‎injuries to the pelvic floor sustained during childbirth‎. ‎Despite the large number of women affected by SUI‎, ‎little is known about the mechanisms associated with the maintenance of urinary continence in women‎. ‎The work in this ‎research ‎focuses on studying the behavior of the bladder and the dynamics of the urine during an increase in abdominal pressure like a cough‎. ‎The computational model is developed by using the Finite Elements Method (FEM) and Fluid-structure interaction (FSI) techniques. ‎The results show a good accordance between the clinical data and predicted values of the computational models. ‎Simulated pressure is more accurate in the model in which non-linear material properties are utilized. The results of the computational methods indicate that by using numerical techniques and simplification of the physics of biological systems, clinical results can be reached in virtual environments in order to understand pathological mechanisms.