Local stabilization of nonlinear discretetime systems with timevarying delay in the states and saturating actuators Abstract   Although most of the control design methods assume unbounded control signals, real systems do have saturating actuators, which may degenerate closedloop performance or even lead to unstable behavior. Additionally, the delay is generally almost ubiquitous in processes, that is also imposing performance and stability constraints. Our main contribution is to provide a controller design methodology for the stabilization of delayed systems under saturating actuators. Specifically, we address the design of nonParallel Distributed Compensation (nonPDC) state feedback fuzzy control laws that locally stabilize a class of nonlinear discretetime systems with state timevarying delay and saturating actuators. The proposed nonPDC control law depends on the current state xk and the state delayed by     d  xc2xaf     samples. Based on the LyapunovKrasovskii approach, we characterize the safe region of initial conditions through two sets: an ellipsoidal one for the current state vector, and another set for the delayed state vectors. Trough two convex optimization procedures, we can maximize the estimate of the region of attraction of the closedloop control system. Additionally, a relaxation method inspired by the FrankWolfe algorithm is introduced, yielding better estimates of the region of attraction. The achievements are compared with other finds in the literature, illustrating the efficiency of this proposal.

On local stability of stochastic delay nonlinear discrete systems with statedependent noise Abstract   We examine the local stability of solutions of a delay stochastic nonlinear difference equation with deterministic and statedependent Gaussian perturbations. We apply the degenerate Lyapunovxe2x80x93Krasovskii functional technique and construct a sequence of events, each term of which is defined by a bound on a normally distributed random variable. Local stability holds on the intersection of these events, which has probability at least     1  xe2x88x92  xcexb3  ,     xcexb3xe2x80xafxe2x88x88xe2x80xaf(0, 1). This probability can be made arbitrarily high by choosing the initial value sufficiently small. We also present a generalization to systems where a condition for stability is expressed in terms of the diagonal part of the unperturbed system, and computer simulations which illustrate our results.