This paper presents some results on absolute sta-x(j), Vi = 1,... n. Inequalities between vectors are componentbilization of nonlinear discrete-time systems under control sat-wise: x < 0 means that x(,) < 0 and x < y means that x(j) -y(i) < urations. The studied control law consists of the feedback of 0. I, denotes the n x n identity matrix.both the states and of the nonlinearity present in the dynamics of the controlled system. Saturations are taken into account II. PROBLEM PRESENTATION by modelling the nonlinear saturated system through deadzone nonlinearities satisfying a modified sector condition. Thus, as for Consider a nonlinear discrete-time system represented by: continuous-time systems, LMI absolute stabilization conditions are proposed for the design of the feedback gains, both in the Xk Axk+G(Zk)+Bsat(uk) (1) local and global stability contexts. Some relations of the proposed Zk LXk results with the dissipativity and passivity theory are included where xk E 9", Uk E 9jm Zk e W and qp( ) --A, B, and a numerical example is reported. G and L are real constant matrices of appropriate dimensions.
The stabilization of a network controlled system including a global time-varying delay is investigated in this note. This delay is considered to be unknown but it is assumed that a bounded error estimate is available. The exponential uncertainty induced by the time-varying delay is decomposed into a sum of a polytopic term and an uncertain bounded term. Sufficient conditions to design a dynamic output feedback controller depending on estimate of the time-varying delay are proposed as LMIs. An illustration shows how our methodology enlarges the design techniques of the literature.
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