Harouna Souley Ali

Unknown inputs functional observers designs for delay descriptor systems

New time and frequency domain designs of unknown inputs functional observers (UIFO) for a class of descriptor systems with a constant time delay are investigated in this paper. The unknown inputs are present in both the state and the measurement equations. The time procedure design is based on the unbiasedness of the estimation error and the Lyapunov Krasovskii stability theory. After given the existence condition of such observers, the gain implemented in the functional observer with internal delay design is obtained in terms of linear matrix inequalities. The particular cases, where the observer is independent of internal delay and where it is independent of delay are also investigated. A design algorithm that summarises the different steps of the UIFO design is proposed. Then, the frequency procedure design is derived from time domain results by applying the factorisation approach, where we define some useful matrix fraction descriptions. Note that the order of this unknown input observers is equal to the dimension of the vector to be estimated. A numerical example is given to illustrate the effectiveness of the presented approach.

An H ∞ adaptive observer design for linear descriptor systems

This paper is devoted to the design of an H∞ adaptive observer for a class of linear descriptor systems in order to estimate simultaneously the system states and its parameters. Based on a mathematical transformation on the system, a new method is presented in order to get an augmented measure matrix from which the observer is built. The existence conditions of the observer are given through matrices equations and are so easily verified via rank conditions. The H∞ observer is then designed using a mathematical parameterization via LMI, in order to ensure the minimization of the disturbances effects on the observation errors. A numerical example is then given to illustrate the design procedure.

Finite-time H_inf functional filter design for a class of descriptor linear systems

In this paper, we design a finite-time H∞ observer. The system under consideration is a linear descriptor system subject to time-varying norm bounded disturbances. The aim of this paper is focused on the design of a state observer which ensures that the estimation error is finite-time bounded and minimizes the effect of the disturbances. A non bias condition is presented for the solvability of this problem, which is reduced to a problem involving linear matrix inequalities (LMIs). Finally, a numerical example is given to show the validity of the proposed methodology.

Almost Sure Exponential Stability of Large-Scale Stochastic Nonlinear Systems

ABSTRACT 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.

A robust reduced order functional H ∞ observer for time delay bilinear systems

This paper proposes a method for the design of a robust functional H∞ observer for a class of time delay bilinear systems. The considered system is affected by norm-bounded uncertainties in the system matrices and an unmeasured perturbations which are of finite energy. The unbiasedness conditions on the nominal part of the error dynamics of the proposed reduced order observer were given by calling an algebraic framework. Since, those conditions are satisfied, and by calling a Lyapunov-krasovskii approach, the stability conditions are obtained through LMI (Linear Matrix Inequality).

Asymptotic stability in probability of a square root stochastic process

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.

Robust reduced order observer for a class of uncertain nonlinear stochastic systems

This paper investigates the robust reduced order observer design for nonlinear stochastic systems with muliplicative noises. The parametric uncertainties are bounded and unstructured. The proposed reduced order observer guarantees that the equilibrium point of the estimation error is almost surely exponentially stable despite of the uncertainties. The observer matrices are computed by solving LMI.

State estimation of a SCARA Robot using sliding mode observers

In this paper a new method of designing a sliding mode observer for SCARA robot is proposed. This method is based on the construction of the singularity subspaces. The algorithm for estimating position and speed of the considered robotic manipulator is presented. Simulation results confirm the validity of our approach.

Sufficient conditions for almost sure exponential stability of large scale interconnected stochastic systems

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.

Controllers Design for Two Interconnected Systems Via Unbiased Observers

Abstract This paper proposes functional observer based controller for each subsystem of two interconnected system. The new approach that we use to express the control error permits to use some results on large scale delay systems to solve the problem. The proposed controllers are free of the interconnection terms, and the observation errors are unbiased. The observers based controllers are designed via some matrices gains which are obtained via LMIs (i.e. via a tractable approach) from the Lyapunov stability results. An algorithm is given for the computation of the solutions. The result can be extended for the H∞ control of linear and nonlinear large scale systems.