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In this paper, a data mining based methodology for process identification from historical data was proposed. Thereon, it considers the phases of process understanding, data collection, data prepara...

This article tackles the problem of high-accurate tracking of the stator currents of a six-phase induction motor in the presence of unknown dynamics such as unmeasurable rotor currents, parameter variation, and disturbances. Since the good features offered by sliding mode theory motivate the community of researchers on control, a time delay estimation based discrete-time super-twisting controller is proposed. First of all, an outer loop is carried out to regulate the speed and to generate the desired stator currents. Second, the inner loop, based on an indirect rotor field-oriented control, is executed based on the developed approach. The structure of the proposed method allows a precise approximation of the unknown dynamics and an accurate tracking and a fast convergence of the tracking error to a neighbor of zero. The design procedure and the stability analysis are detailed for the stator currents closed-loop system. Experimental tests have been performed on a six-phase induction motor to demonstrate the effectiveness of the developed discrete approach. In addition, the performances obtained are compared to the ones obtained using the discrete-time sliding mode with time delay estimation. The results obtained highlighted the satisfactory stator currents tracking performance in transient conditions and steady state and under different sampling times, parameters mismatch, and load and no-load conditions.

In industrial smelters, sulfuric acid is manufactured using the elemental sulfur in a series of three-unit operations: elemental sulfur oxidation, sulfur dioxide catalytic conversion, and sulfur trioxide absorption. The sulfur oxidation, which is the basic step in this process, is generally performed under a sulfur combustion furnace that ensures the production of the process gas stream, which will be the main supply stream to the other unit operations. In this paper, a dynamic model is developed based on the fundamental mass and energy balance, including the sulfur oxidation and the dynamic flow behavior aspects within the furnace. The obtained model is simulated in the Matlab/Simulink environment and data from an industrial plant were used to validate the model. The simulation results and the plant measurement comparison showed an accuracy of 96%, with a mean absolute error of 16.12 °C and a root mean square error of 23.27 °C. Afterwards, the effect of different operating conditions and disturbance parameters on the sulfur combustion furnace performance were studied. Finally, the relationship and a correlation between the temperature and sulfur dioxide molar fraction at the outlet of the furnace were investigated for industrial use.

The bulk port operations are given a growing attention for their important role in the global supply chain in different industries (mining, energy ...). To guarantee their competitiveness, the efficient management of port logistics, including yard side management is crucial. In this paper, we consider a real-word storage space allocation problem at an export bulk terminal. We formulate the problem as a mixed integer linear program and we propose a heuristic method to solve large scale data sets. Both the model and the heuristic can help the yard planner to test different scenarios and provide better stock yard plan, which is a first step toward improving the management of port operation in the bulk terminal under study.

This study deals with the problem of controlling rotor speed and stator currents of an asymmetrical six-phase induction machine with uncertain dynamics, disturbances, and unmeasurable rotor currents and proposes a robust non-linear variable structure controller. First of all, an outer control loop based on a proportional–integral regulator is performed to control the rotor speed and to construct the desired stator current references. Then, the inner loop is performed based on the proposed method that combines the time delay estimation method and discrete sliding mode control based on exponential reaching law. This structure allows an accurate and simple estimation of uncertainties and rotor currents, a high-tracking precision, a convergence of the stator currents to their known desired references in finite-time and chattering reduction. The design procedure is detailed step by step and the stability analysis and the convergence time are established for the current closed-loop system. Experimental work was carried out on an asymmetrical six-phase induction motor drive to show the effectiveness and performance of the proposed robust non-linear discrete method. The results obtained highlighted the good tracking performance of the stator currents.

In the mining industry, thickeners are used to increase density of slurries by removing water. When a thickener is in operation, the underflow slurry density should follow a given setpoint and stay inside a boundary layer. In general, thickeners are manually controlled. However, industrial experience has shown that manual control is not sufficient. For this reason, an advanced process control strategy is proposed in this paper. On the one hand, using historical data, a linear dynamic model of the studied thickener is developed. In this regard, data is collected, prepared, and data informativity is studied to ensure model identifiability and interpretability. On the other hand, a model predictive control is designed to control the process by manipulating the feed and the underflow slurry flowrates. The simulation results show that the method can be successfully used to control the underflow slurry density in the presence of feed variations and unmeasured disturbances.

Sulfuric acid is a basic chemical used intensively in many industrial processes. To produce the sulfuric acid, there are two major processes: the lead chamber process and the current contact process. The first step in the latter process consists of burning sulfur in the air to form sulfur dioxide. In this paper, modeling and simulation of an industrial sulfur burning unit are performed. For the modeling task, an adiabatic conversion reactor was used for the sulfur burner, a centrifugal pump for the liquid sulfur pump, and an air compressor for the air supply. To simulate the model, the Unisim Design R451 simulator was used. Then, the simulation results were validated using industrial data. In addition, a parametric study was performed to analyze the effects of the inputs' variations on the sulfur burner outlet. The proposed model can be used to develop a digital twin of the studied sulfur burner to perform real-time simulations and test new control and optimization strategies.

This work investigates the problem of controlling robot manipulators with matched and mismatched uncertainties. To this end, a robust backstepping combined with super-twisting controller is developed to guarantee the convergence of the joint position states to their desired references. The proposed control technique allows the rejection of the uncertainties while eliminating the sliding mode's famous drawback that is the chattering. Based on recursive Lyapunov function, sufficient condition is set to ensure the closed-loop system stability. Finally, simulation and experimental works were carried out respectively on a two degrees-of-freedom robot model and on the seven degrees-of-freedom ANAT modular robot to verify the performance and the robustness of the developed control strategy.

Flow behavior of solid-liquid flow systems depends on the solids’ properties, the carrier fluid and the interactions between the two phases. The solids’ properties of slurry pumping systems such as granulometry and density change as a function of time and location. The above-mentioned changes impact directly the slurry pumping flow rate. In this paper, a dynamic model of an industrial mixing tank with a slurry centrifugal pump is proposed. The dynamic model takes into account the different parts of the pump; the hydraulic part, the induction motor and the system head. A graphical method is then used to estimate the hydraulic part and the induction motor parameters. Regarding the system head, the model is generalized for both homogeneous and heterogeneous flows. The overall model is simulated using MATLAB/Simulink software and validated through a comparison between the results obtained and the real industrial data of a slurry mixing and pumping unit. Finally, the effects of density and level variations on the flow dynamic behavior are studied.

Tubular exchangers are among the most widely used exchangers in the industrial sector. It is essentially divided into two most common categories: shell and tube heat exchangers (STHE) and coaxial exchangers. It is also possible to consider a STHE as a sum of simple coaxial tubes, which greatly facilitates the understanding and modeling of STHE. Currently, the optimization of heat transfer in exchanger is a recurring problem for thermal engineers. Therefore, several numerical and experimental studies have been carried out. In this paper, the experimental and numerical study of heat transfer and dynamic behavior analysis of tubular heat exchanger (HE) is carried out in order to optimize the energetic performance of the exchanger. Experimentally, two configurations of co-current and counter-current exchangers have been investigated. Theoretically, the dynamic modeling and simulation of the HE was performed using Matlab/Simulink, Unisim-Design simulator, ANSYS-Fluent and Comsol multiphysics commercial software. The models' results were validated experimentally with very good agreement of 99%. Finally, the developed models are confronted to an industrial case of sulfuric acid cooling unit. The results obtained have a very good accuracy of 98.99% with the real plant data.

Multiphase induction generators are gaining popularity in wind energy systems for their robustness, reliability and fault-tolerant behavior when compared to the famous three-phase ones. This work proposes an advanced robust nonlinear control strategy for a multiphase induction generator in a variable speed wind energy conversion system. The considered structure in this paper consists of a six-phase induction generator and two conventional three-phase two-level voltage source converters. The stator currents of the structure are regulated using the proposed method that consists of a time delay estimation-based modified super-twisting. On one hand, and a proportional-integral regulates the speed in an outer control loop. On the other hand, the proposed method regulates the stator currents in an inner control loop. The stability analysis of the closed-loop error dynamics is proved using a quadratic Lyapunov function. Finally, numerical simulations have been carried out on a model of a real six-phase induction generator to show the good features of the designed method.

In this paper, an Optimal Super-Twisting Algorithm (OSTA) with time delay estimation is designed based on Input/Output feedback linearization for uncertain robot manipulators. The design procedure consists on three steps. Firstly, an Input/Output feedback linearization is applied to transform the nonlinear model into a linear equivalent one. Secondly, by defining a quadratic performance, an optimal sliding surface will be designed. Finally, a super-twisting algorithm with time delay estimation is proposed for high accuracy tracking trajectory. Lyapunov theory is used to prove the finite-time convergence of the sliding surface and its derivative. This structure is used to estimate unknown dynamics and to reduce the control effort and the chattering phenomenon.

This paper proposes a super-twisting algorithm (STA) with time delay estimation (TDE) for the problem of high-accuracy tracking trajectory of robotic manipulators in the presence of uncertainties and unexpected disturbances. The TDE method is known for it capability to estimate uncertainties simply without an exact knowledge of the system dynamics. Using the estimated uncertainties, the control law is then designed based on STA to ensure robustness, finite-time convergence and chattering reduction. The stability analysis of the closed-loop system and the finite-time convergence are proved using Lyapunov theory. In order to show the effectiveness of the proposed method, simulations and experimental results were carried out on a 2-DOF rigid robot manipulator and on the 7-DOF ANAT robot arm, respectively.

One of the most efficient approaches to control a multiple degree-of-freedom robot manipulator is the virtual decomposition control (VDC). However, the use of the re- gressor technique in the conventionnal VDC to estimate the unknown and uncertaities parameters present some limitations. In this paper, a new control strategy of n-DoF robot manipulator, refering to reorganizing the equation of the VDC using the time delay estimation (TDE) have been investigated. In the proposed controller, the VDC equations are rearranged using the TDE for unknown dynamic estimations. Hence, the decoupling dynamic model for the manipulator is established. The stability of the overall system is proved based on Lyapunov theory. The effectiveness of the proposed controller is proved via case study performed on 7-DoF robot manipulator and com- pared to the conventionnal Regressor-based VDC according to some evalution criteria. The results carry out the validity and efficiency of the proposed time delay estimation- based virtual decomposition controller (TD-VDC) approach.

Control of uncertain nonlinear systems is one of the main topics in automation, control problem. However, uncertainties caused by uncertain parameters, load variations, unmodeled dynamics and external disturbances affect the control performance. This paper investigates the problem of high accuracy joint space trajectory tracking. A discrete-time second order sliding mode combined with time delay estimation is designed to make the joint positions track a desired trajectory with high accuracy. In addition, sufficient condition assuring convergence of the error to zero in finite time based on Lyapunov theory is presented. Experiments on a 7-DOF ANAT robot arm are presented to verify the performance of the proposed controller.

In this work, a time delay estimation based optimal conventional and second order sliding mode stator currents controller are proposed and compared for a six-phase induction machine fed by voltage source power converters. In a first step, the speed is regulated in an outer loop using a proportional-integral controller. Then, in a second step, the stator currents are controlled in an inner loop using the proposed methods. On one hand, the first method is a combination of time delay estimation with optimal first order sliding mode with exponential reaching law. On the other hand, the second method is a combination of time delay estimation with optimal super-twisting control. Based on Lyapunov theory, the stability of the stator currents closed-loop error dynamics is demonstrated and sufficient conditions of stability are determinate. As a case example, numerical simulations have been conducted on an asymmetrical six-phase induction machine to demonstrate the good features of the developed nonlinear controllers.

The inverse kinematic analysis is required in many technical applications. Due to the non linearity of the system, resolving the Inverse Kinematics (IK) for robotic system becomes more challenging problem. In this chapter, the problem of IK for medical application is faced, based on human lower limb as being the three arm robotic system depending on the physiological constaints. A system analysis is carried out specially in three dimensionnel space. The developed forward kinematic model leads to define the feasible workspace of the human leg in the considered configuration. A constructive algorithm to compute the optimal IK of robot system is outlined, based on human performance measure that incorporates a new objective function of musculoskeletal discomfort. The effectiveness of the proposed approach is tested, and the algorithmic complexity is finally discussed.

The object of this paper is to study the problem of robust stabilizability for a class of continuous-time Linear Systems with Markovian Jumps (LSMJ) and saturated input. Sufficient conditions for stochastic stabilizability with constrained control input are given in terms of Linear Matrix Inequalities (LMIs). The approach gives a direct expression of the linear state feedback controller that respects the condition of saturation. Also, the robustness of these systems for four types of structural uncertainties: (1) matching conditions, (2) norm bounded, (3) value bounded and (4) linear combinations is treated. Finally, numerical examples are given to illustrate the usefulness of the proposed results.

In this chapter, a robust backstepping sliding mode controller with time delay estimation method is presented for high accuracy joint space tracking trajectory of robot manipulators with unknown dynamics and external disturbances. The proposed method is based on backstepping scheme, on a switching function and on a time delay estimation in the final step. This structure is used to estimate unknown dynamics and disturbances, to adapt the switching gains in term of the error and its first time derivative and to reduce the control effort and the chattering phenomenon. Lyapunov theory is used to establish sufficient condition that ensures the stability of the closed-loop system. The proposed controller is simulated on a two-link robot and implemented in real time on the 7-DOF ANAT robot to show the effectiveness regarding unknown dynamics and external disturbances and chattering reduction.

This work investigates the problem of finite-time position and attitude trajectory of quadrotor unmanned aerial vehicle systems based on a modified second order sliding mode algorithm. The selected algorithm is a modified super-twisting with both nonlinear and linear correction terms. It ensures robustness against unknown dynamics and perturbations and allows fast finite-time convergence even when the trajectories of the considered system are far from the user-chosen switching surface. In addition, this algorithm is very attractive since it solves the major problems of the first and second order sliding mode, namely, the chattering phenomenon and the required unavailable information for practical implementation. To show the effectiveness of the used modified structure of the super-twisting algorithm, simulation results are presented for the considered quadrotor system.

The aim of this chapter is to presents a Kinematic analysis of a Cable-Driven Robot for rehabilitation use of human lower limb, by taking into account the constraints required by the entrainment system and the mobile platform (human leg). The proposed approach is focused on optimizing the manipulability and the human performance of the human leg, as being a physiologically constrained three-link arm. The obtained forward kinematic model leads to define the feasible workspace of the human leg in the considered configuration. Using an effective optimization-based human performance measure that incorporates a new objective function of musculoskeletal discomfort, and the mapping relation between articular joints actuator, length cables and articular joint mobile platform, the optimal inverse kinematic (IK) model is obtained.

A robust nonlinear backstepping technique with Lagrange’s extrapolation and PI compensator is proposed in this chapter for high accuracy trajectory tracking of robot manipulators with uncertain dynamics and unexpeted disturbances. The proposed controller is synthesized by using Lagrangian extrapolation method with PI compensator to estimate the uncertainties and disturbances and to deal with the effect of hard nonlinearities caused by the estimation error while nonlinear backstepping technique is used to ensure good tracking. The stability analysis is accomplished recursively using appropriate Lyapunov functions candidate. As a result, the proposed control technique shows better performances via experimental results on a 7-DOF robot arm in comparison with the classical backstepping and sliding mode control.

This paper investigates the problem of stator current control in presence of uncertainties and unmeasurable rotor current for a six-phase induction motor drive. An inner control loop based on a robust discrete-time sliding mode with time delay estimation method is proposed to ensure the finite-time convergence of the stator currents to their desired references while the proportional-integral controller is used for the outer speed control. Sufficient conditions are established to ensure the stability of the closed-loop system. Simulation results were carried out to verify the performance of the proposed robust control strategy for a six-phase induction motor drive.

The paper presents a robust sliding mode with time delay estimation method for controlling the attitude of a tri-rotor unmanned aerial vehicle (UAV) in presence of uncertainties and disturbances. The proposed control algorithm allows high accuracy tracking since a good disturbance estimation is provided using time delay estimation method and allows chattering reduction. The stability analysis of the closed-loop system is presented using the theory of Lyapunov. Finally, two numerical simulations are presented in the presence of disturbances to show the effectiveness of the proposed nonlinear control scheme.

This paper examines the problem of output feedback control of a Takagi-Sugeno (TS) fuzzy fishery system. The considered system is the continuous age structured model of an exploited population that includes a nonlinear stock-recruitment relationship. The effort is used as control term, the age classes as states and the quantity of captured fish per unit of effort as measured output. In order to stabilize the stock states around the references equilibrium, which means biologically the sustainability of the fish stock, the output feedback controller is adopted, rather than a controller based on the state observer. An algorithm based on the linear matrix inequality is proposed to compute the static output feedback gain. Simulation results of the continuous fishery systems confirm the effectiveness of the proposed design. Fisheries management can be investigated using modern control theory.Jurdjevic-Quinn based method does not handle model with n2, our proposed method does.The suggested control law guarantees the biological sustainability of the fish stock. This paper examines the problem of output feedback control of a Takagi-Sugeno (TS) fuzzy fishery system. The considered system is the continuous age structured model of an exploited population that includes a nonlinear stock-recruitment relationship. The effort is used as control term, the age classes as states and the quantity of captured fish per unit of effort as measured output. In order to stabilize the stock states around the references equilibrium, which means biologically the sustainability of the fish stock, the output feedback controller is adopted, rather than a controller based on the state observer. An algorithm based on the linear matrix inequality is proposed to compute the static output feedback gain. Simulation results of the continuous fishery systems confirm the effectiveness of the proposed design.

Multiphase induction motor drives have gained popularity due to their fault tolerance and better power/current distribution per phase which are very attractive for industrial applications. Current control strategies with the estimation of unmeasurable variables (typically rotor variables) has been recently proposed for multiphase induction drive. This paper proposes a novel current control based on super-twisting algorithm with time delay estimation for a five-phase induction motor drives. This method considers the estimation of rotor variables and disturbances, and also ensures the stability by using Lyapunov theory. Simulation results are provided to show the effectiveness of the proposed method and also to compare with other controllers such as a proportional-integral and a model-based predictive controllers.

In this paper, a new posture prediction method is proposed and evaluated on human leg, as being a physiologically constrained three-link arm. The main posture prediction solution is focused on optimizing the manipulability and the human performance of the leg. The forward kinematics is used to define the feasible workspace of the human leg in sagittal plane. Using an effective optimization-based human performance measure that incorporates a new objective function of musculoskeletal discomfort, the optimal posture is obtained.

This paper proposes a non-singular terminal sliding mode combined with time delay controller for fast tracking trajectory of uncertain second-order nonlinear systems in presence of external disturbances. The motivation for using Non-Singular Terminal Sliding Mode (NSTSM) mainly relies on its appreciable features, such as simplicity of design and implementation, high precision and fast convergence. However, the NSTSM problem is the well-known chattering, which degrades the controlled system. Then, using the time delay to estimate uncertainties and disturbances allows chattering reduction. The stability and the robustness of the proposed controller are verified by using the classical Lyapunov criterion. The proposed controller is implemented in real time on the seven-degrees-of-freedom (7-DOF) ANAT robot arm and compared with the Sliding Mode with Time Delay Control (SMTDC) with classical sliding surface to prove its superiority.

In this paper, a new method is proposed to design an observer for a nonlinear and uncertain system describing a continuous stage structured model of a harvested fish population. The aim is to get an estimation of the biomass of fishes by stage class. In the studied model the fishing effort is considered as a control term, the stage classes as states and the quantity of captured fish as a measured output. A Takagi–Sugeno multimodel first represents the uncertain non-linear model. Next, we develop a technique for designing a multimodel observer corresponding to this system, which attenuates the effect of modelling uncertainties and measurement noise on the state estimation. The design conditions are given in linear matrix inequalities (LMIs) terms that can be solved efficiently using existing numerical tools. The validity of the proposed method is illustrated by the simulation results.

This paper proposes a second order sliding mode combined with time delay controller to track a desired trajectory for robot manipulators with unknown dynamics and external disturbances. The motivation for using second order sliding mode (SOSM) mainly relies on its appreciable features, such as high precision and elimination of chattering in addition that it ensures robustness. However, the SOSM problem is that the unknown dynamics and the disturbances may be amplified, which makes the system unstable. Then, using the time delay allows to benefit from the robustness of the second order sliding mode while reducing its major drawback. The stability and the robustness of the proposed controller is verified by using the classical Lyapunov criterion. The proposed controller is implemented in real time on the seven-degrees-of-freedom (7-DOF) ANAT robot arm and compared with the sliding mode with time delay control (SMTDC) to prove its superiority.

This chapter introduces two controllers design for the trajectory tracking of robot manipulators with unknown dynamics and external disturbances, including: First Order Sliding Mode with Time Delay Control (FOSMTDC), Second Order Sliding Mode with Time Delay Control (SOSMTDC).

This paper proposes a robust nonlinear current controller that deals with the problem of the stator current control of a six-phase induction motor drive. The current control is performed by using a state-space representation of the system, explicitly considering the unmeasurable states, uncertainties and external disturbances. To estimate these latter effectively, a time delay estimation technique is used. The proposed control architecture consists of inner and outer loops. The inner current control loop is based on a robust discrete-time sliding mode controller combined with a time delay estimation method. As said before, the objective of the time delay estimation is to reconstruct the unmeasurable states and uncertainties, while the sliding mode aims is to suppress the estimation error, to ensure robustness and finite-time convergence of the stator currents to their desired references. The outer loop is based on a proportional-integral controller to control the speed. The stability of the current closed-loop system is proven by establishing sufficient conditions on the switching gains. Experimental work has been conducted to verify the performance and the effectiveness of the proposed robust control scheme for a six-phase induction motor drive. The results obtained have shown that the proposed method allows good performances in terms of current tracking, in their corresponding planes.

This paper deals with the robust H∞-control problem for uncertain continuous-time linear time-delay systems with Markovian jumping parameters. Based on Lyapunov functional approach, a sufficient condition that assures the robust stochastic stabilizability and preserves the H∞-disturbance attenuation for the uncertain class of linear time-delay systems with Markovian jumping parameters is established. The uncertainties considered in this paper are of the norm-bounded type. A numerical example is given to demonstrate the usefulness of the results.

In this paper, we study the problem of robust stabilization of discrete-time linear systems with Markovian jumping parameters (DTLSMJP) with norm bounded uncertainties. A sufficient condition guaranteeing te robust stability of the uncertain discrete-time linear systems with Markovian jumping parameters (UDTLSMJP) is presented, which is in terms of a set of coupled discrete-time algebraic Riccati inequalities (IEqs). Finally, a numerical example is given to show the potential of the proposed technique.

In this paper, we study the problem of robust stabilizability of the class of uncertain linear systems with Markovian jumping parameters. Under the assumption of complete access to the continuous state, the stochastic stabilizability of the nominal system and the boundedness of the system's uncertainties, sufficient conditions which guarantee the robust stability of the uncertain systems are presented, which are in terms of a set of coupled algebraic Riccati equations. A numerical example is given to illustrate the potential of the proposed technique.

This paper deals with the robustness of the class of uncertain linear systems with Markovian jumping parameters (ULSMJP). The uncertainty is taken to be time-varying norm bounded. Under the assumptions of the boundedness of the uncertainties and the complete access to the system's state and its modes, a sufficient condition for stochastic stabilizability of this class of systems is established. An example is provided to demonstrate the usefulness of the proposed theoretical results.

This paper deals with the mean square stochastic stability of the class of linear time-delay systems with Markovian jumping parameters. A delay-independent sufficient condition for checking the stochastic stability of this class of systems is established. A numerical example is given to show the usefulness of the proposed theoretical results.

This paper deals with the class of linear time-delay systems with Markovian jumping parameters (LTDSMJP). We mainly extend the stability results of the deterministic class of linear systems with time-delay to this class of systems. A delay-independent necessary condition and sufficient conditions for checking the stochastic stability are established. A sufficient condition is also given. Some numerical examples are provided to show the usefulness of the proposed theoretical results.

In this paper, we deal with the robust stabilizability of the class of uncertain linear time-delay systems with Markovian jumping parameters and unknown but bounded uncertainties. Under the assumption of the complete access to the continuous state, the stochastic controllability of the nominal system and the boundedness of the system’s uncertainties, sufficient conditions which guarantee the robustness of the stability of this class of systems are given. The control law which guarantees the robustness of the stabilizability is linear-type or saturation-type. An example is presented to illustrate the usefulness of the proposed theoretical results.

The automatic classification of non stationary signals is an important practical goal in several domains. An essential classification task is to allocate the incoming signal to a group associated with the kind of physical phenomena producing it. In this paper, we present a modular system composed by three blocs: 1) Representation, 2) Dimensionality reduction and 3) Classification. The originality of our work consists in the use of a new wavelet called "Ben wavelet" in the representation stage. For the dimensionality reduction, we propose a new algorithm based on the random projection and the principal component analysis., {"references":["S. Abeysekera and B. Boashash, \"Methods of signal classification using\nthe images produced by Wigner distribution\" Pattern Recognition Letters, 12,\npp. 717-729, 1991.","L. Atlas, J. Droppo and J. McLaughlin, \"Optimizing time-frequency\ndistributions for automatic classification\" In the International Society for\nOptical Engineering, 1997.","M. Davy, C. Doncarli, and G. F. Boudreaux-Bartels, \"Improved\noptimization of time-frequency based signal classifiers\" IEEE Sig. Proc. Let,\n8, pp. 52-57, 2001.","F. Hlawasch and G. F. Boudreaux-Bartels, \"Linear and quadratic timefrequency\nsignal representations\" IEEE Sig. Proc. Mag, 9, pp. 21-67, 1992.","A. Papandreou-Suppappola, F. Hlawasch and G. Boudreaux-Bartels,\n\"Quadratic time-frequency representations with scale covariance and\ngeneralized time-shift covariance: a unified framework for the affine,\nhyperbolic and power classes\" Digital signal Processing, 8, pp.3-48, 1998.","L. Cohen, \"Generalized phase-space distribution functions\" J. Math. Phys,\n7, pp. 781-786, 1966.","L. Cohen, \"Time-frequency analysis\" Prentice Hall, 1995.","O. Rioul and P. Flandrin, \"Time-scale energy distributions : a general class\nextending wavelet transforms\" IEEE Trans on Signal Processing, 40, pp.\n1746-1757, 1992.","P. Flandrin, \"Temps-fréquence\", Academic Press, 1998.\n[10] F. Hlawasch, A. F. Papandreou-Suppappola and G. Boudreaux-Bartels,\n\"The power classes of quadratic time-frequency representations : a\ngeneralization of the hyperbolic and affine classes\" In 27th Asilomar Conf on\nSignals, Systems and computers, Pacific Grove, CA, 1265-1270, 1993.\n[11] F. Hlawasch, A. F. Papandreou-Suppappola and G. Boudreaux-Bartels,\n\"The hyperbolic class of quadratic time-frequency representations. Part II:\nSubclasses, intersection with affine and power classes, regularity unitarity\"\nIEEE Trans on Signal Processing, 45, pp. 303-315, 1997.\n[12] A. Papandreou-Suppappola, F. Hlawasch and G. Boudreaux-Bartels,\n\"Power class time-frequency representations: interference geometry,\nsmoothing and implementation\" In IEEE Symposium on Time-Frequency and\nTime-Scale Analysis, Paris, pp.193-196, 1996.\n[13] I. Daubechies, \"Ten lectures on wavelets\", SIAM, Philadelphia, Pa,\n1992.\n[14] C. Torrence and G. P. Compo, \"A practical guide to wavelet analysis\"\nBull. Amer. Meteor. Soc, 79, pp. 61-78, 1998.\n[15] M. Benbrahim, K. Benjelloun and A. Ibenbrahim, \"Discrimination des\nsignaux sismiques par réseaux de neurones artificiels\" In Proc of 3èmes\njournées nationales sur les systèmes intelligents: théorie et applications, Rabat,\nMorocco, pp. 62-66; 2004.\n[16] R. Bellman, \"Adaptive control processes: A guided tour\" Princeton\nUniversity Press, Princeton, 1961.\n[17] W.B. Johnson and J. Lindenstrauss, \"Extensions of Lipshitz mapping\ninto Hilbert space\" In Conference in modern analysis and probability, volume\n26 of Contemporary Mathematics, Amer. Math. Soc, pp. 189-206, 1984.\n[18] I. T. Jolliffe, \"Principal component analysis\", Springer-Verlag, 1986.\n[19] J. E. Jackson, \"A user's guide to principal components\", John Wiley,\nNew York, 1991.\n[20] M. Benbrahim, A. Daoudi, K. Benjelloun and A. Ibenbrahim,\n\"Discrimination of seismic signals using artificial neural networks\" In Proc of\nthe second world enformatika congress, WEC'05, Istanbul, Turkey, pp 4-7,\n2005.\n[21] A. Daoudi, M. Benbrahim and K. Benjelloun, \"An intelligent system to\nclassify leaks in water distribution pipes\" In Proc of the second world\nenformatika congress, WEC'05, Istanbul, Turkey, pp 1-3, 2005."]}

In this paper, we deal with the robust stabilizability of the class of uncertain linear time-delay systems with Markovian jumping parameters and unknown but bounded uncertainties. Under the assumption of the complete access to the continuous state, the stochastic controllability of the system and the boundedness of the system's uncertainties, sufficient conditions which guarantee the robustness of the stability of this class of systems are given. A feedback control laws are used (linear-type and saturation-type).