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The control and command of singular systems of non-regular type pose very complex problems for automation engineers. The classic concepts of controllability are not applicable because of the non-regularity of the response of such systems whose internal states are no longer controllable in the temporal or frequency plane. New concepts are rather considered such as R-Controllability and Imp-Controllability combined with $$H_2/H_\infty $$ H 2 / H ∞ type stabilization approaches. This paper proposes a new synthesis of a $$H_2/H_\infty $$ H 2 / H ∞ controller, written in terms of LMI-like matrix inequalities, dedicated to this type of system. The simulation results, of the controller synthesized on methanation plant are encouraging and have led to better performance compared to other scientific publications in the field.

In this work, the authors are considering the problem of compensation of harmonic current absorbed by a non-linear load from a three-phase grid voltage. The objective is twofold: the first is to reduce cost and control complexity by avoiding proportional–integral regulators and optimising measurement instrumentation while ensuring inverter capacitor voltage self-balance and the second is to provide a robust control strategy against power grid problems. Without measuring current and capacitor voltages, the proposed control strategy generates accurate control signals able to ensure flying capacitor inverter self-balance and full compensation of harmonics whatever the grid voltage problem. In this regard, the robustness of the proposed control against power grid problem such as sag, swell, grid voltage unbalance, and frequency variation have been tested while proving its efficiency to compensate for harmonic currents and ensuring capacitor voltage natural balance even in transient regimes. During balanced and unbalanced loads, the proposed method has exhibited an excellent transient response, represented by capacitor voltages tracking to their reference in the presence of large variation in the load. Finally, effectiveness of the proposed control strategy is verified by numerical simulations as well as realistic experiments, and its merits are showed in comparison with other methods.

This paper discusses the hardware and control system design of the asymmetric cascade multilevel inverter. The asymmetric cascaded multilevel inverter structure is adopted to minimize bridges, gate drive circuits and DC power source number. Therefore, the proposed structure is able to generate higher voltage at higher speed with low switching losses and high efficiency. Selective Harmonic Elimination (SHE) based on Newton-Raphson (N-R) algorithm is developed to calculate a switching angle for a range of modulation index to control asymmetric cascade multilevel inverter. Simulation results prove that Newton-Raphson technique is more effective than genetic algorithm (G-A) and equal calculated switching angles method (ECSA). A comparison between the algorithm performance for 9-level asymmetric cascade H-bridge inverter control was evaluated and experimentally tested on FPGA-based prototypes.

In this article, Newton–Raphson optimization-based selective harmonic elimination pulse width modulation is investigated for open-loop control of flying capacitor multilevel inverter. Proposed control strategy has allowed giving up current and voltage measurement instrumentations and sensors used in case of closed loop–based control. Proposed control strategy generates accurate switching angles, capable to balance flying capacitor voltage and eliminate lower order harmonics considering load power factor variation. Algorithm performances are verified by simulation and experiments, and obtained results prove that proposed technique does effectively eliminate specific harmonics and balance capacitor voltages while getting inverter output voltage with desired number of levels.

In this paper, SHE based on Newton–Raphson algorithm is used for open-loop control of flying capacitor multilevel inverter. Without measuring current and capacitor voltages, as well as not using any controller and voltage feedback, proposed control strategy generates accurate switching angles, capable of balancing flying capacitor voltage and eliminates lower order harmonics while considering load power factor variation. Efficiency and robustness of proposed algorithm are verified by simulation and experiments. Results show that proposed method does effectively eliminate specific low-order harmonics, and inverter output voltage is resulted in low total harmonic distortion with desired number of levels and balanced capacitor voltages.

The mathematical models used in the estimation of GHI on the Earth's surface are inconvenient because they always assume that the sky clarity index is constant. Hence, these models are often confronted with long-period empirical ground measurements that may exceeds 11 years. The impact of cloud cover on an electric power generation site is a very critical parameter for installing a solar power plant and evaluating its productivity. The state of knowledge about the sun influence, the greenhouse effect on climate change, and cloud occurrence can’t be described in a mathematical or numerical model.Therefore, in this paper, we propose the use of Deep-Learning techniques to predict any site’s productivity by analyzing its potential insolation. We also suggest the analysis of the ground and satellite- based measurements collected over 30 years. We propose the estimation of future climate change affecting cloud cover.

In this paper, two issues are discussed in a PV pumping system. Firstly, an evaluation of super capacitor is studied to reassure the storage of electrical energy and solve the intermittence problem of photovoltaic energy production in dark periods. Secondly, a fuzzy logic controller (FLC) is proposed to stabilize, on the one hand, the DC motor speed around a preferred level by the control of duty cycle of DC buck boost converter. On the other hand, FLC serves to control the charge and discharge of super capacitor according to the sunlight levels and its state of charge. In this framework, a complete photovoltaic pumping system model is simulated in MATLAB Simulink to discuss the run results at different levels of sunshine.

A new approach is presented for sensor fault detection reconstruction and state estimation. The system considered is linear polytopic parameter-vary ing (LPV) system. The main idea is the design of a novel robust adaptive observer based on and polyquadratic formulation with a new set of relaxation. Sufficient conditions are given by a set of Linear Matrix Inequalities (LMI) in order to guarantee the stability of the system and the asymptotic convergence of the fault error. A simulation example has been studied to illustrate the proposed methods by detecting constant and variable sensor fault.

In this paper, we study the problem of state estimation and both actuator and sensor fault detection for Linear Polytopic Parameter-Varying (LPV) system. The contribution of this work consists on t...

In this paper a control strategy using backstepping technique for multilevel inverter based active power filter control is developed. Performances comparison between backstepping strategy and PI regulators based methods is provided. Simulation results prove the robustness and accuracy of proposed technique compared with conventional methods.

The results obtained by using an existing model to estimate global solar radiation (GHI) in three different locations in Tunisia. These data are compared with GHI meteorological measurements and PV_Gis satellite imagery estimation. Some statistical indicators (R, R2, MPE, AMPE, MBE, AMBE and RMSE) have been used to measure the performance of the used model. Correlation coefficient for the different stations was close to 1.0. The meteorology and satellite determination coefficient (R2) were also near 1.0 except in the case of Nabeul station in which the meteorology measurements (R) were equals to 0.5848 because of the loss of data in this location due to meteorological conditions. This numerical model provides the best performance according to statistical results in different locations; therefore, this model can be used to estimate global solar radiation in Tunisia. The R square values are used as a statistical indicator to demonstrate that the model’s results are compatible with those of meteorology with a percentage of error less than 10%.

Having enough knowledge of the basic solar components, including Direct Normal Irradiation (DNI), Diffuse Horizontal Irradiance (DHI) and Global Horizontal Irradiation (GHI), is greatly significant to concentrated solar power (CSP) projects. (DNI), the amount of direct irradiance received on a plane normal to the sun, is of remarkable usefulness to CSP technologies around the world. However, in Tunisia, the field of solar energy generation faces twofold challenges. First, the unique type of solar concentrating collectors works only on global horizontal irradiation (GHI) which is the geometric sum of DNI and DHI. Second, these collectors are available in a limited number of locations.Regarding this additional review of hourly DNI, our approach to the real time assessment of the clear sky DNI gives a good estimation in the worst case the mean absolute error equal to 40 W/m² for hourly values in comparison to the measured data.

Background Several climatologists and experts in the renewable energy field agree that GHI and DNI calculation models must be revised because of the increasingly unpredictable and powerful climatic disturbances. The construction of analytical mathematical models for the prediction of these disturbances is almost impossible because the physical phenomena relating to the climate are often complex. We raise the question over the current and future PV system’s sustainable energy production and whether climate disturbances will be affecting this sustainability and resulting in supply decline. Methods In this paper, we tried to use deep learning as a tool to predict the evolution of the future production of any geographic site. This approach can allow for improvements in decision-making concerning the implantation of solar PV or CSP plants. To reach this aim, we have deployed the databases of NASA and the Tunisian National Institute of Meteorology relating to the climatic parameters of the case study region of El Akarit, Gabes, Tunisia. In spite of the colossal amount of processed data that dates back to 1985, the use of deep learning algorithms allowed for the validation of the previously made estimates of the energy potential in the studied region. Results The calculation results suggested an increase in production as it was confirmed by the 2019 measures. The findings obtained from the case study region were reliable and seemed to be very promising. The results obtained using deep learning algorithms were similar to those produced by conventional calculation methods. However, while conventional approaches based on measurements obtained using hardware solutions (ground sensors) are expensive and very difficult to implement, the suggested new approach is cheaper and more convenient. Conclusions In the existence of a protracted controversy over the hypothetical effects of climate change, making advances in artificial intelligence and using new deep learning algorithms are critical procedures to strengthening conventional assessment tools of the production sites of photovoltaic energy and CSP plants.

This paper represents an electrical modeling of a photovoltaic water pumping system composed of photovoltaic panels. The system reassures electrical energy generation applying a DC buck converter in order to supply a DC motor to pump water. Known for its optimal electrical and physical properties, the super capacitor is integrated into the PV pumping system to allow storing electrical energy and powering the pumping motor at nights and cloudy days. The implementation of the perturbation and observation algorithm in the DC buck converter reassures the system’s operation around the maximum power point produced by the photovoltaic panel. Moving from quantity problem to quality problem, several internal and external factors can infect the stability of the PV pumping system and disrupt its operation around nominal point. On account of this, a pole placement technique is proposed in this paper. This technique is advocated not only for its simple processing and rapid execution, but also for being based on the conversion of the electrical model of the PV pumping system into a mathematical model that comprises matrix equations. This energy conversion process allows variations in output values in proportion to the input evolution along with positioning the system’s poles in the stable points of the S-plane. The equation of this technique applied to the photovoltaic pumping system is indicated in this paper having its program created in Matlab and installed in PLC S7-200 on account of its ability to monitor the inputs instantaneously and modify the outputs in a way proportional to the installed program. Subsequently, the validation of the robustness of this technique is reassured by the comparison between the simulation in Matlab and the experimental tests carried out in sunny periods having the engine powered by photovoltaic panels, and shaded periods where power supply is reassured by the super capacitor.

In this paper, we treat the problem of both state estimation and fault detection of nonlinear systems. Those systems could be described by a poly-quadratic Linear Parameter-Varying (LPV) form. A new adaptive observer is developed in terms of Linear Matrix Inequalities (LMI) technique. A feasible algorithm is developed to compute the designed parameters. This algorithm provides more flexibility and mitigates the conservatism of quadratic approach. Finally, simulation results are presented to illustrate the efficiency of the proposed method..

This paper is an extension of work originally presented in conference name. The goal is to propose new fault detection and fault isolation techniques for a polytypic linear parameter-varying system (LPV). In this work, an adaptive observer design is formulated for a given polyquadratic Lyapunov function. Subsequently, new sufficient conditions are given in terms of Linear Matrix Inequalities (LMIs). To show the effectiveness of the proposed algorithm, an illustrative example is included.

Newton-Raphson-based flying capacitor multilevel inverter modeling is investigated for capacitor voltage balancing. Without using voltage feedback, Newton-Raphson method determines the best switchi...

Municipal solid waste management (MSWM) is one of the major environmental issues in Tunisian cities. Rapid growth in urbanization and population rates and the changes in people’s lifestyle have prompted a dramatic increase quantity and a significant shift in the composition of municipal solid waste. There is insufficient data concerning the quantities and the composition of waste streams along with the absence of a comprehensive complete overview and a wider perspective of MSWM potential that provides detailed information at region and city level. As a result, it is still impossible for the scientific community and the authorities to provide synergetic schemes to tie the problems of MSWM with how to integrate economically feasible and environmentally sustainable practices holistically. In the present study, an attempt has been made to provide a comprehensive overview of MSW, through a qualitative (compositional) and quantitative (parametric) characterization of the generated total waste generated in Tunisian cities. A 1-year research survey was conducted in seven regions in Tunisia (Great Tunis, Northeast, Northwest, Midwest, Mideast, Southwest, and Southeast) that cover the 24 provinces of the country. Collected samples revealed that the distribution of waste by region was defined by the region’s demographic, economic, and industrial status. Approaches of possibly more efficient procedures that can be undertaken to improve MSW collection are discussed. At a final stage and based on the potential of biogas calculated in the seven regions, we suggest that the scientific community and the authorities should introduce applicable schemes to valorize MSW through generating biogas as a renewable energy.

Without measuring current and capacitor voltages, SHE based on Newton raphson algorithm is investigated in open loop control of flying capacitor multilevel inverter for determining the best switching angles for balancing capacitor voltages and eliminating certain harmonic orders considering power factor variation. Simulation results show that the proposed method does effectively eliminate specific low order harmonics and the output voltage is resulted in low total harmonic distortion with balanced flying capacitors.

The work develloped in this paper treat the problems of simultaneous actuator and sensor fault estimation for an Air Craft System. The original system can often be modeled as polytopic linear parameter varying (LPV) plants for which some estimation techniques of fault and state still hard to solve. Here, we propose a new approach to design an adaptive observer based on quadratic Lyapunov approach. The solution is described as an optimization problem formulated in terms of Linear Matrix Inequalities (LMI) techniques. A simulation design shows that the new algorithm yields to reliable state estimation and simultaneous fault detection of the LPV model of Air Craft System which illustrate the validation of the proposed method.

In this paper, a serial/parallel cascaded H-bridge (CHB) multilevel inverter is presented. The topology has the advantage of reduced number of switching devices, DC-sources and gate driver circuits. Consequently, cost and complexity are greatly minimised, providing the same number of output voltage levels even more compared to conventional structures and other topologies given in some recent literatures in which authors have proposed new topologies with reduced circuit devices count (RDC). The main contribution of this work is the ability to choose a set of harmonic order to be eliminated; in other similar works, PWM technique is only capable to minimise total harmonic distortion (THD) without eliminating selected harmonic which require a complex output filter. The feasibility and effectiveness of the proposed topology is evaluated with intensive simulation study and experimentally tested on a prototype using a field-programmable gate array (FPGA) to implement N-R algorithm for inverter selective harmonic elimination (SHE) control.

This paper proposes a synthesis of a dynamic controller under constraints. It is based on model predictive control (MPC) approach and resolution of a convex optimisation problem with linear matrix inequalities (LMI). The controller guarantees the closed-loop stability for polytopic time-varying uncertain systems. Conditions are provided for the controller design based on the parameter dependent Lyapunov functions (PDLF). A new demonstration is developed based on the relaxation technique, to include a slack variables Gi. The new LMI's formulation offers an additional degree of freedom for the controller design. Input and output constraints are also taken into account during the design of the controller. This approach allows varying and adjusting the dynamic of system by taking into account input/output constraints.

Available solar radiation is an important source of renewable energy that determines Tunisia's productivity but has been poorly characterized. Measured solar radiation datasets are generally not available for long periods. This paper studied the method of estimates for solar radiation based on satellite imagery and on the measured data by the national institute of meteorology. Data collected from the year 2015 in three different locations in Tunisia. The objectives of this study are: a) Assess of monthly global solar radiation using data of meteorology for three stations. b) Compare measured data with two different geostationary satellites imagery in order to validate the good estimation of the satellite imagery. c) Reduce the uncertainly of the use of satellite imagery long-term solar resource by validate the estimated data with those measured by the pyranometer from the meteorological station.

To maximize the production of electrical energy in photovoltaic plants, the best solution is to use sun tracking systems whose panels are permanently exposed to solar radiation to ensure the best angle of inclination. These systems are expensive, their implementation is difficult, and their maintenance is complicated. The fixed inclination of the solar panels is easy to implement but its profitability is minimal. To solve this dilemma, the researchers propose to shift the panel’s angle of inclination over predetermined periods. In many countries, weather data measurements are either unavailable or lacking. So to fill this gap, we propose in this paper the development of mathematical models to calculate the best angle of inclination and the period of poise of this angle (month, season or other duration). The theoretical results obtained are validated by experimental tests and are conducted in three regions of Tunisia (North, Center and South). The objective is to determine, for each region, the optimal angle and the duration needed before switching to the next angle depending on the installation of fixed PV panels shortfalls.

The study of the solar radiation is the starting point of any investigation for a new energy, to study and search the best location to install a PV system. A very important factor in the assessment of solar potential is the availability of data for global solar radiation that must be coherent and of high quality. In this paper, we analyze the estimation result of the monthly global solar radiation for three different locations, Bizerte in Northern Tunisia, Kairouan in Middle Eastern Tunisia, and Tozeur in Southern Tunisia, measured on the surface by the National Institute of Meteorology and the meteorological year irradiation based on satellite imagery result PVGIS radiation databases. To get the right measurements with minimum error, we propose a numerical model used to calculate the global solar radiation in the indicated three sites. The results show that the model can estimate the global solar radiation (kWh/m²) at a specific station and over most area of Tunisia. The model gives a good estimation for solar radiation where error between the measured values and those calculated are negligible.

Photovoltaic energy is very important to meet the consumption needs of electrical energy in remote areas and for other applications. Energy storage systems are essential to avoid the intermittent production of photovoltaic energy and to cover peaks in energy demand. The super capacitor, also known as electrochemical double layer capacitor, is a storage device which has a very high power density compared to conventional battery and is capable of storing a large amount of electrical energy in short time periods, which reflects its interest to be used for the storage of photovoltaic energy. From this principle, this paper represents a three-branch RC model of super capacitor to describe its different dynamics of operation during the charging, discharging and rest phases. After having validated the good functioning of this model with the experimental study of Zubieta, The super capacitor performance has been demonstrated and compared with a conventional battery in a photovoltaic converter chain to power AC machine.

A very important factor in the assessment of solar potential for the installation of photovoltaic plants is the availability of global irradiation data measurements. Such data must be collected over a period of time longer than 11 years and must be accurate. In some countries, it is difficult to have databases of these measures. To overcome this problem, we propose, the use of numerical models to estimate the monthly, seasonally and annually solar energy irradiation (global diffuse and direct solar radiation), especially on tilted surface.The results obtained from the numerical models are compared to the data collected from three regions on Tunisia: Bizerte (in the north), Nabeul (near to the north east) and Djerba (in the south).The actual measurements taken from the meteorological stations and the measurements generated by the numerical models are very close.After the validation of the numerical models, we tried to calculate the best tilt angle for each period of the year to position a photovoltaic panel, in a given region, to reach maximum energy recovery.The practical validation, of the optimal tilt angle search and the adequate period, was conducted at the Research and Technology Center of Energy of Borj Cedria. The obtained results are satisfactory and prove the reliability of the constructed numerical models. Keywords: Solar radiation estimation, Inclined surface, Optimum tilt angle, Gained energy

Predictive control presents a solution to the problem of the trajectory generation for a humanoid robot. This control strategy is introduced by Katayama 13 and improved by Kajita 1 , in those literatures, the theory of predictive control is used to calculate the trajectory of the mass center of the cart table to track a reference trajectory and give it for the ZMP. However this control has an inconvenience such as the non respect of real-time constraints, due to the computation time and the output response establishing. In this paper we propose the predictive PID controller that imitate the calculated time and reduce the complexity of the control algorithm. The aim of this new control approach for biped robot is to make walking smoother and more efficient.

This paper treats the estimation of the state of a nonlinear system with unknown input. The nonlinear system is described by a multimodel with unknown function of activation but depending only on the state. The method of design of the multiobserver is described by using the second method of Lyapunov and their candidate functions. The sufficient obtained stability conditions are expressed in terms of Linear Matrix Inequalities (LMI) and are obtained first using the Lyapunov quadratic functions and secondly by using Lyapunov polyquadratic functions. This latter technique seems to be less conservative and less constraining than the first. Illustrative examples are presented in this paper.

Having regard to the large application of the inverted pendulum in robotic system, this study is interested in controlling this process with two strategies of controls. The first proposed control is the state feedback with an observer based on the Generalized Predictive Control (GPC) algorithm. In the second proposed control we used the characteristic of predictive control GPC to improve the performance of the classical PID controller. The obtained results have been discussed and compared; the simulation results obtained by the predictive PID control are mentioned.

This study presents a new approach for modeling and controlling of a compass gait biped robot based on the use of the switched systems. The linearization of the equations stemming from the formalism of Lagrange allows the construction of a set of local models used to describe the behavior of this non linear system. The selection of each model depends on its activation function depending on the system states. The synthesis of the stability of the walking robot is based on the use of second method of Lyapunov. The synthesis approach leads to a set of bilinear matrices inequalities non resolvable by actual numerical solvers. To come over these difficulties, some relaxations are brought to get useful and exploitable numerical solutions.

In this paper, the problem of fault isolation and detection is treated for a particular class of linear polytopic parameter-varying system (LPV). In this context, an adaptive observer design is formulated for a given polyquadratic Lyapunov function. As a result, new sufficient conditions are given in terms of Linear Matrix Inequalities (LMIs), which guarantee asymptotic convergence to zero of the estimation error, and to detect and isolate actuator faults. A tentative application was made to show the effectiveness of the proposed algorithm.

In this paper a new topology of cascaded H-bridge (CHB) multilevel inverter employing less number of switches, is presented.

This paper deals with the control design of an asymmetrical cascaded multilevel inverter. This structure therefore provides the capability to produce higher voltages at higher speeds with low switching frequency which has inherent low switching losses and high converter efficiency. Selective harmonic elimination(SHE) for asymmetrical multilevel CHB inverter control is proposed. The technique utilized in the estimation of switching angles involves Firefly Algorithm (FFA). Compared to Newton Raphson algorithm (NR), FFA is more robust and entails less computation time. Simulation results prove the effectiveness of FFA technique compared to NR algorithm. The proposed method does effectively eliminate a number of specific low order harmonics, and the output voltage is resulted in low total harmonic distortion. FFA and NR algorithm for asymmetrical cascaded H-bridge nine level inverter control are experimentally tested on a prototype using FPGA.

This paper presents an algorithm of a robust controller used for the stabilization of biped robot walking gait. The robot is described by a kajita's model with norm bounded uncertainties to ensure a more realistic numerical model. The proposed robust dynamic controller relies on the use of predictive control theory (MPC) and the resolution of a convex optimization problem with Linear Matrix Inequalities (LMI) at every sampling period. The generated control law allows a realtime working robot even in rough ground or unknown environment.

the analysis and control of delayed systems are becoming more and more research topics in progress. This is mainly due to the fact that the delay is frequently encountered in technological systems. Most control command laws are based on current digital computers and delays are intrinsic to the process or in the control loop caused by the transmission time control sequences, or computing time. In other hand, the controls of humanoid walking robot present a common problem in robotics because it involves physical interaction between an articulated system and its environment. This close relationship is actually a common set of fundamental problems such as the implementation of robust stable dynamic control. This paper presents acomplete approach, based on switched system theory, for the stabilization of a compass gait robot subject to time delays transmission. The multiple feedback gains designed are based on multiple linear systems governed by a switching control law. The establishment of control law in real time is affected by the unknown pounded random delay. The results obtained from this method show that the control law stabilize the compass robot walk despite a varying delay reaching six times sampling period.

Problem statement: More advanced control techniques have been developed in recent decades following the great progress of calculation s means. Without considering the constraints on system variables, the response of controlled system moves away from the desired response. Hence the control strategy must provide the ability to integr ate these constraints in the design phase of the controller. Approach: This study presents a design of robust dynamic con troller which was based on the control strategy MPC for an uncertain discrete system described by a multimodel by solving an optimization problem. The Model Predictive Control (MPC) strategy uses a dynamic model of the process in order to predict its future behavior. Th is control strategy, that we propose, makes it poss ible to integrate these constraints in the design phase of the controller. The design of the robust dynamic controller must maintain the stability and performa nce of the system in the presence of uncertainties. The principle of this method was to solve, at each calculation step, a convex optimization problem tha t calculates the matrices characterizing the dynamic controller. LMI formulation of the constraints, on process variables, was introduced into the design p hase of the dynamic controller robust. The optimization study was also implemented in the MATLAB software and simulation studies had been presented. Results: Simulation results had proved the effectiveness of this study. The robust dynamic controller designed for uncertain systems guarantee s stability in closed loop systems by integrating constraints on system variables. Conclusion: The described approach explain how to integrate constraints, MPC type, during the phase of design o f the robust controller: the simulation concluded o n a benchmark proof the powerful of this approach.

Problem statement: The analysis and control of delayed systems are be coming more and more research topics in progress. This is mainly du e to the fact that the delay is frequently encounte red in technological systems. This can affect their sig nificantly operations. Most control command laws are based on current digital computers and delays a re intrinsic to the process or in the control loop caused by the transmission time control sequences, or computing time. The delay may affect one or more states of the considered system. It may also a ffect the establishment of the command. Several studies have investigated the stability of delay sy stems under the assumption that the delay is a vari able phenomenon; such variation is considered to be bounded or limited to facilitate analysis of the system . In this study we propose a modelling of delayed sys tem by using the multimodels and switched system theory. The analysis of stability is based on the u se of second Lyapunov method. The issued stability conditions are expressed as Bilinear Matrix Inequal ities impossible to resolve. That's why we propose the same original relaxations to come over this dif ficulty, an example of induction machine is given t o illustrate over approach. Approach: We propose to use the control theory developed for switched systems to synthesis a control laws for the stabili sation of delays system. Results: We stabilize the induction machine around many operating points despite the non linearities. Conclusion: The developed method is less conservative and less pess imistic than the used classical methods.

In this paper, a comparison between two observers has been made; an adaptive observer and multiobserver for linear time-varying system. This observer has been designed to estimate simultaneously the state space and faults detection (sensors and actors). The convergence of the adaptive observer is implemented under certain condition. An example of a drying blower system is used to show the effectiveness of the proposed observers.

Problem statement: The estimation of states and the unknown inputs of a nonlinear system described by a multimodel are done by a multiobserver. The stabilization of the multiobserver calls upon uses both quadratic and no quadratic functions of Lyapunov. Although the stabilization using the quadratic approach is interesting from the point of view implementation, the step showed its limits for the multimodel. However, the problem paused by the quadratic method lies in the obligation to satisfy several LMI with respect to the same Lyapunov matrix P, these results are shown very conservative. Approach: To reduce the conservatism of the quadratic approach we propose another approach which is exclusively based on Lyapunov piecewise quadratic functions. The conditions obtained by the stabilization of the multiobserver are expressed in term of matrix inequalities with constraints on the matrices rank. Results: The estimation of both states and unknown inputs of a multimodel using the quadratic approach per pieces leads to results less conservative than the quadratic approach. Academic examples illustrate the robustness of the piecewise quadratic approach. Conclusion: In this article we proposed new sufficient conditions of stability of a multiobserver able to the estimation of states and unknown inputs of a nonlinear system describes by a multimodel subjected to the influence of the unknown inputs. The study in was carried out by considering two approaches. The first approach is based on Lyapunov quadratic functions; it is significant to note the great difficulty in finding satisfying results by this approach for the multimodel systems. For this reason we proposed an approach based on piecewise quadratic functions which led to interesting results (proposition 1) and less conservative than the quadratic approach. The conditions suggested in this article concern both the multiobserver stabilization and the estimation of states and the unknown inputs of a multimodel with measurable variables of decision (µξ(k)). The synthesis of a multiobserver with no measurable variables of decision is not approached. This point can constitute an interesting prospect for this study.

In this work, we propose a novel robust dynamic controller in order to stabilize a walking biped robot with input and output constraints. Firstly, the trajectory of the robot is generated via the Zero Moment Point method based on the resolution of a convex optimization problem with Linear Matrix Inequalities. Then, the tracking of a referential trajectory is insured by the design of an optimal dynamic controller with predictive control theory. The synthesized dynamic controller allows the Lyapunov stability of the robot's walk. Moreover, it ensures the reducing of the overshoot and undershoot of the output signal, difficult to be adjusted by classical methods. This work is validated by a simulation via Matlab of some illustrative examples and results highlight the efficiency of the proposed study.

This work aims to design an optimal dynamic controller to stabilize the walk of a biped robot even in the presence of input and output constraints. In a first time, the robot's trajectory is generated via the Zero Moment Point criterion based on the resolution of a convex optimization problem with Linear Matrix Inequalities. In a second time, the tracking of a reference trajectory is insured by the design of an optimal dynamic controller based on the predictive control theory. The synthesized dynamic controller allows for the Lyapunov stability of the robot's walk. Moreover, it ensures the reducing of the overshoot and undershoot of the output signal that are difficult to be adjusted by classical methods based on solving the algebraic Riccati equation. This study is validated by a simulation via Matlab of some illustrative examples. Results are presented to prove the effectiveness of the proposed work.