Stabilization of Discrete-Time Systems With Multiple Actuator Delays and Saturations

Abstract

This paper studies the problems of global and semi-global stabilization of discrete-time linear systems with multiple input saturations and arbitrarily large bounded delays. By developing the methodology of truncated predictor feedback (TPF), state feedback control laws using only the current states of the systems are constructed to solve these problems. The feedback gains are dependent on the delay information of the open-loop system and thus are referred to as delay-dependent feedback. A method for determining the exact condition such that the resulting closed-loop system is asymptotically stable is also presented. Moreover, if the delays in the system are time-varying or even unknown, a modified delay-independent TPF is also established to solve the concerned problems. Numerical example has been worked out to illustrate the effectiveness of the proposed approaches.

Semi‐global output feedback control for nonlinear systems with uncertain time‐delay and output function

“…Some interesting problems remained as follows: (i) Some semi-global results such as [20][21][22] on the systems with input delay have been obtained, but these papers only consider linear systems; a problem is: can these results be extended to nonlinear systems with unknown input delay and output function? (ii) Recently, many results on stochastic nonlinear systems with y D x 1 , for example, [23][24][25][26][27][28][29][30][31][32][33][34], have been achieved; the second problem is whether some results can be obtained for stochastic nonlinear systems with unknown output function.…”

“…Assumption 1 contains more general nonlinearities which permit linear and high-order nonlinear time-delay terms. While [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] only consider nonlinear systems without time delay, [20][21][22] only consider linear time-delay systems.…”

Pseudo‐predictor feedback control of discrete‐time linear systems with a single input delay

“…The stability analysis in [33] was then significantly simplified in [32] by designing F as (35). The underlying mechanism in the previous low gain feedback design in [33] and [32] was latterly revealed in [28] by establishing a general methodology referred to as truncated predictor feedback (TPF), which was originally proposed in [23] for continuous-time time-delay systems (for TPF for continuous-time time-delay systems, see [23] and p. 14 in [30] for detailed introduction). The idea of TPF is that, as long as F satisfies (33), the memory terms in the traditional predictor feedback (4) are a high-order infinitesimal and can be dropped out to result in a finite dimensional controller.…”

“…The resulting controller is also finite dimensional and is thus easy to implement.We consider stabilization problems of discrete-time linear systems with a single input delay. Discrete-time systems have received considerable attention in the literature because of their wide applications in engineering with the development of computer techniques ([8, 14, 25-27] and [28]). The aim of the present paper is to extend the results in [24] to discrete-time setting.…”

Bounded control of feedforward time‐delay systems with linearized systems consisting of chain of oscillators

“…Delays and control constraints are ubiquitous in practical systems. 1,2 Ignoring time delays/constraints in the design of circuits and systems will degrade the system performances and may even lead to instability. For this reason, research interest on these two topics has increased over the past two decades.…”