Multirate sampled‐data stabilization for a class of low‐order lower‐triangular nonlinear systems

Abstract

Summary This paper investigates the problem of sampled‐data controller design for a class of lower‐triangular systems in the p‐normal form (0<p<1). A multirate digital feedback control scheme is proposed to achieve the global strong stabilization of the sampled‐data closed‐loop system under some assumptions. In the design of the controller, the input‐Lyapunov matching strategy and multirate control approach are combined to obtain better stabilizing performance. Unlike the design method based on the approximate discrete‐time model, our controller is obtained from the exact discrete‐time equivalent model, which does not need to be computed completely. The approximate multirate digital controllers are proved to be effective in the practical implementation. It is shown that, compared with the emulated control scheme, our controller may provide faster decrease of Lyapunov function for each subsystem. This will lead to allow large sampling periods. An illustrative example is provided to verify the effectiveness of the proposed control scheme.

Dynamic output feedback stabilization for a class of nonsmooth stochastic nonlinear systems perturbed by multiple time-varying delays

“…Next, we will prove that formula (15) still holds for the (x 1 , x 2 , • • • , x i )-subsystem. In fact, Choose a Lyapunov-Krasoviskii functional for the subsystem…”

“…[24] investigated the finite-time stabilization problem by developing an efficient recursive design procedure, and Ref. [15] addressed the GSS of a class of LOSs by proposed a multi-rate sampling controller. In the stochastic setting, Ref.…”

“…Although the some stabilization results with regard to LOSs have been obtained in Refs. [5,15,24,32], it is clearly that they cannot be suitable for LOSs with time delays. Third, there is no doubt that the simultaneous appearance of multiple time-varying delays, unmeasured state variables, stochastic disturbances and low-order nonlinear terms will greatly increase the difficulties of solving the problem.…”

“…• The powers of chained integrators for the loworder systems studied in the published papers, such as [5,15,24,32], are restricted to the positive odd rational numbers. The present paper removes this restriction.…”