Stability Criteria For Discrete-time Systems Research Articles

Enhanced Stability Criteria for Discrete-time Systems with Time-varying Delay

The stability problem of discrete-time linear systems with interval time-varying delays is investigated in this paper. According to the latest summation inequality technique, an improved free-matrix-based summation inequality is proposed in this paper. In order to make full use of the improved inequality to bound the upper bounds of the difference Lyapunov-Krasovskii functional (LKF), an augmented LKF with some extra status information is constructed. A new delay-range-dependent stability criterion is derived in the form of linear matrix inequalities (LMIs) via the modified LKF approach. The criterion is less conservative than some existing results. Finally, some standard numerical examples are presented the effectiveness of the proposed approach.

Stability and Stabilization of Discrete-Time T–S Fuzzy Systems With Time-Varying Delay via Cauchy–Schwartz-Based Summation Inequality

This paper proposes new stability and stabilization conditions for discrete-time fuzzy systems with time-varying delays. By constructing a suitable Lyapunov–Krasovskii functional and introducing a new summation inequality based on the inequality of Cauchy–Schwartz form, which enhances the feasible region of the stability criterion for discrete-time systems with time-varying delay, a stability criterion for such systems is established. In order to show the effectiveness of the proposed inequality, which provides more tight lower bound of a summation term of quadratic form, a delay-dependent stability criterion for such systems is derived within the framework of linear matrix inequalities, which can be easily solved by various effective optimization algorithms. Going one step forward, the proposed inequality is applied to a stabilization problem in discrete-time fuzzy systems with time-varying delays. The advantages of the proposed stability and stabilization criteria are illustrated via two numerical examples.

Improved Delay-Dependent Stability Criteria for Discrete-Time Systems with Time-Varying Delays

This paper considers the stability problem for discrete-time systems with interval time-varying delays. By construction of a suitable Lyapunov–Krasovskii (L–K) functional and utilization of Finsler’s lemma, novel delay-dependent criteria for asymptotic stability of the systems are established in terms of linear matrix inequalities (LMIs) which can easily be solved by various effective optimization algorithms. Three numerical examples are given to illustrate the effectiveness of the proposed method.

Use of the Nyquist Stability Criterion in the Design of Interactive Audio Digital Filters

Interactive audio processing systems sometimes include user-controlled digital filters, whose response is obtained by interpolating between different transfer functions. Audible artifacts produced by these filters are caused by migration across the unit circle of the zeros in their transfer function, depending on the interpolation parameter values. There are cases in which the Nyquist stability criterion for discrete-time systems can turn useful to inspect, and possibly modify the trajectories of such zeros. After a general discussion, two examples are illustrated in which Nyquist stability is used to optimize the response of filters realizing a linear interpolation between two transfer functions.

The Delay-Dependent for Discrete-Time Systems

Problem statement: This study is concerned with the problem of delay- dependent stability analysis for discrete-time systems with interval-li ke time-varying delays. Conclusion/Recommendations: The 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. into account. It is worth noting that the closed-lo op system resulting from a delayed controller is actua lly a time-delay system. Therefore, stability results o f time-delay systems could be applied to design time- delayed controller. The present study a new Lyapunov functional, an improved delay-dependent stability criterion for discrete-time systems with time-varying delays is presented in terms of LMIs. It is shown that the obtained result is less conservative than those in. Example is providing, respectively, to demonstrate the reduced conservatism of the proposed stability crit erion and the effectiveness of the proposed design method . Preliminaries: Lemma 2.1 (Agarwal, 2000) the zero solution of difference system is asymptotic stabili ty if there exists a positive definite function n

Delay-Dependent $\hbox{H}_{\infty }$ Filter Design for Discrete-Time Fuzzy Systems With Time-Varying Delays

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper investigates delay-dependent <formula formulatype="inline"><tex Notation="TeX">$\hbox{H}_{\bm\infty }$</tex></formula> filter design problems for discrete-time fuzzy systems with time-varying delays. First, a novel delay-dependent piecewise Lyapunov–Krasovskii functional (DDPLKF) is proposed in which both the upper bound of delays and the delay interval are considered. Based on this DDPLKF, the delay-dependent stability criteria for discrete-time systems with constant or time-varying delays are obtained, respectively. Then, delay-dependent full-order and reduced-order <formula formulatype="inline"><tex Notation="TeX">$\hbox{H}_{\bm\infty }$</tex></formula> filter design approaches are proposed. The filter parameters can be obtained by solving a set of linear matrix inequalities (LMIs). Simulation examples are also given to illustrate the performance of the proposed approaches. It is shown that our approaches are less conservative and that the corresponding <formula formulatype="inline"><tex Notation="TeX">$\hbox{H}_{\bm\infty }$</tex></formula> filters can achieve better performance than the existing approaches. </para>

Elliptic ball stability criterion for discrete-time systems

The elliptic ball criterion is proved for the discrete-time non-linear feedback control equation p(6) x+ BM(t)q(B)x = 0, in which θxlpar;t) = x( t + 1). It is a geometrical condition for stability and instability which reduces to the well-known circle criterion in. the special case when the matrix M(t) is a scalar. For a certain class of equations the elliptic ball criterion is shown to be both necessary and sufficient for the existence of a special kind of quadratic Lyapunov function. The analogy with differential equations is found to fail in one respect