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**Improved stability criterion and its applications in delayed controller design for discrete-time systems.**
*(English)*
Zbl 1152.93453

Summary: This paper is concerned with the problem of delay-dependent stability analysis for discrete-time systems with interval-like time-varying delays and the problem of stabilization for discrete-time linear systems via time-delayed controllers. The first problem is solved by applying a novel Lyapunov functional, and an improved delay-dependent stability criterion is obtained in terms of a linear matrix inequality. Based on this, a sufficient condition for the solvability of the second problem is presented. The reduced conservatism of the proposed stability result is shown through a numerical example, while the applicability of the time-delayed controller design method is demonstrated by an inverted pendulum system.

### MSC:

93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |

93C55 | Discrete-time control/observation systems |

### Keywords:

delay-dependent stability; discrete-time systems; stabilization; time-varying delays; time-delayed controllers
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\textit{B. Zhang} et al., Automatica 44, No. 11, 2963--2967 (2008; Zbl 1152.93453)

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### References:

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