Harouna Souley Ali

In this paper, we investigate the design of a positive functional observer-based controller for positive linear systems subject to unknown inputs. We propose a new approach to numerically compute the controller, which is obtained via a function of the state to be estimated with the same order as the controller. The positive observer-based controller, is obtained into two steps. First, we search for a positive state feedback gain for the design of a control law such that the closed-loop is positive and asymptotically stable. This synthesis of state-feedback gain is solved using Linear Programming (LP) technique. Then, we search in a second step for a positive functional observer-based controller permitting to reconstruct this control law, and so to estimate only a functional of the state useful for control purposes. The observer is positive, that is, it ensures the nonnegativity of the estimated states. The proposed procedure is based on the positivity of an augmented system composed of dynamics of both considered system and proposed observer-based controller and also, on the unbiasedness of the estimation error by the resolution of Sylvester equation. Then existence conditions of such observer-based controller are formulated in terms of linear programming (LP) problem, where we use the Perron-Frobenius theorem applied to Metzler matrices. An algorithm that summarizes the different steps of the designed positive controller for positive linear systems is given. Finally, a numerical example and simulation results are given to illustrate the effectiveness of the proposed method.

This paper deals with the design of a positive functional H∞ filter-based controller for positive linear systems subject to bounded energy disturbances. We propose a new approach to numerically compute the controller, which is obtained via a function of the state to be estimated with the same order as the controller. The positive filter-based controller is obtained into two steps. First, we search for positive state feedback gain for the design of a control law such that the closed-loop is positive, stable and ensures an H∞ performance requirement. This design of state-feedback gain is solved via constrained Linear Matrix Inequalities (LMIs). Then, we search in a second step for a positive functional filter-based controller permitting to reconstruct this control law, and so to estimate only a functional of the state useful for control purposes. The filter is positive, that is, it ensures the nonnegativity of the estimated states. The proposed procedure is based on the positivity of an augmented system composed of dynamics of both considered system and proposed filter-based controller and also, on the unbiasedness of the estimation error by solving a Sylvester equation. Then we derive conditions for the establishment of such filterbased controller in terms of an optimization problem, that can be solved via constrained LMIs. An algorithm that summarizes the different steps of the designed positive controller for positive linear systems is given. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

This contribution deals with the study of the almost sure exponential stability of large-scale stochastic systems with multiplicative noises. Under a Lipschitz-like assumption, it is proven that this stability is guaranteed if each “diagonal” subsystem is almost surely exponentially stable.

This paper addresses the problem of the design of an adaptive observer for a class of time delay systems, in order to give a suitable estimation of the system states and its unknown parameters simultaneously. Based on a descriptor LPV system approach, we propose a simple full order adaptive observer via Linear Matrix Inequalities (LMI's). Those LMI's permit to fulfill the conditions of the estimation errors stability, relying on Krasovskii Lyapunov approach for time delay systems.

In this paper, we deal with asymptotic stability in probability of a class of stochastic systems, which is described by a stochastic differential equation having a square root on the diffusion part. This type of equations are usually used for the modeling of some systems such as population dynamics. A sufficient condition which ensures the asymptotic stability in probability of this class of systems is given using a Lyapunov approach.

This contribution deals with the study of the almost sure exponential stability of large scale stochastic systems with multiplicative noises. Under some assumption, it is proven that this stability is guaranteed if each “diagonal” subsystem is almost surely exponentially stable.

This contribution deals with the study of the behavior of stochastic systems with multiplicative noise in presence of external disturbances. Sufficient conditions for exponential disturbance rejection are given. They are based on inequalities expressed in terms of Lyapunov functions. Via a bound of the exponential exponent of the solution, a given decay rate of the convergence of the solution is guaranteed.

This paper deals with the observer-based compensator design for bilinear systems. A saturated quadratic control law and a linear control are combined with a funtional LPV (Linear Parameter Varying) observer. We use two kind of controls to have the advantages of both command strategy and to avoid their disadvantages. The closed loop stability is achieved using results on large scale systems and LMI (Linear Matrix Inequality) tools.