Stability Analysis Of2-D Discrete Systems With State Saturation

In2-D discrete-time systems, the nonlinearities consist of the nonlinear constraints of the system state and control input etc. The saturated nonlinearity is one of the most common phenomenon, which inevitably leads to the instability of the systems and even results in the zero input cycle-limited. Also, the uncertainties and time-delays of the transmission data are the main reasons leading to the instability of the systems. In this thesis, the problem of the robust stability is investigated for the state saturation2-D discrete-time systems described by Roesser model. Moreover, the problem of stability is studied for state saturation2-D discrete-time systems described by the Fornasini-Marchesini model.Firstly, the problem of the robust stability is investigated for the uncertain state saturation2-D discrete-time systems described by Roesser model. The uncertain matrices are assumed to have the strong structured uncertainty. By using the Lyapunov method, a sufficient condition is given to guarantee the global asymptotic stability of the systems by constructing an enhanced inequality based on a non-negative scalar β. Accordingly, an algorithm is designed, where the problem of stability is transformed to test the feasibility problem of the linear matrix inequality (LMI). Finally, a numerical example is presented to illustrate the effectiveness of the proposed algorithm.Secondly, the problem of the global asymptotic stability is studied for state saturation2-D discrete-time systems described by the Fornasini-Marchesini second-type model. By introducing the parameter s, the systems are transformed to the2-D discrete-time systems with partial state saturation. By applying the Lyapunov method and introducing an enhanced inequality based on a non-negative scalar β, a new criterion is given to ensure the global asymptotic stability of systems. By using the LMI technique, an algorithm is designed to test the stability criterion of systems. Finally, a numerical example is given to show the validity of the proposed algorithm. Thirdly, by applying the Lyapunov functional method, the problem of global asymptotic stability is investigated for state saturation2-D discrete time-delay systems described by the Fornasini-Marchesini second-type model. Anew sufficient condition is given to ensure the global asymptotic stability of the addressed systems.