This paper investigates the problem of global stabilization by state and output-feedback for a family of for nonlinear Riemann-Liouville and Caputo fractional order time delay systems written in triangular form satisfying linear growth conditions. By constructing a appropriate Lyapunov-Krasovskii functional, global asymptotic stability of the closed-loop systems is achieved. Moreover, sufficient conditions for the stability, for the particular class of fractional order time-delay system are obtained. Finally, simulation results dealing with typical bioreactor example, are given to illustrate that the proposed design procedures are very efficient and simple.
The problem of observer design for a class of nonlinear discrete-time systems with time-delay is considered. A new approach of nonlinear observer design is proposed for the class of systems. Based on differential mean value theory, the error dynamic is transformed into linear parameter variable system. By using Lyapunov stability theory and Schur complement lemma, the sufficient conditions expressed in terms of matrix inequalities are obtained to guarantee the observer error converges asymptotically to zero. Furthermore, the problem of observer design with affine gain is investigated. The computing method for observer gain matrix is given and it is also demonstrated that the observer error converges asymptotically to zero. Finally, an illustrative example is given to validate the effectiveness of the proposed method.