scholarly journals A Simplified Descriptor System Approach to Delay-Dependent Stability and Robust Performance Analysis for Discrete-Time Systems with Time Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Fengying Xu ◽  
Daxin Li
Keyword(s):  
Performance Analysis ◽  
Discrete Time ◽  
System Approach ◽  
Descriptor System ◽  
Linear Matrix ◽  
Quadratic Cost ◽  
Discrete Time Systems ◽  
Delay Dependent ◽  
Time Systems ◽  
Delay Dependent Stability

A simplified descriptor system approach is proposed for discrete-time systems with delays in terms of linear matrix inequalities. In comparison with the results obtained by combining the descriptor system approach with recently developed bounding technique, our approach can remove the redundant matrix variables while not reducing the conservatism. It is shown that the bounding technique is unnecessary in the derivation of our results. Via the proposed method, delay-dependent results on quadratic cost andH∞performance analysis are also presented.

scholarly journals New Delay-Dependent Robust Stability Criterion for LPD Discrete-Time Systems with Interval Time-Varying Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Narongsak Yotha ◽  
Kanit Mukdasai
Keyword(s):  
Robust Stability ◽  
Discrete Time ◽  
Model Transformation ◽  
Linear Matrix ◽  
Time Varying ◽  
Interval Time ◽  
Discrete Time Systems ◽  
Delay Dependent ◽  
Parameter Dependent ◽  
Time Systems

This paper investigates the problem of robust stability for linear parameter-dependent (LPD) discrete-time systems with interval time-varying delays. Based on the combination of model transformation, utilization of zero equation, and parameter-dependent Lyapunov-Krasovskii functional, new delay-dependent robust stability conditions are obtained and formulated in terms of linear matrix inequalities (LMIs). Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

Criteria for stability of uncertain discrete-time systems with time-varying delays and finite wordlength nonlinearities

2017 ◽  
Vol 40 (9) ◽  
pp. 2868-2880 ◽  
Author(s):  
Siva Kumar Tadepalli ◽  
V Krishna Rao Kandanvli ◽  
Abhilav Vishwakarma
Keyword(s):  
Discrete Time ◽  
Time Varying ◽  
Stability Criteria ◽  
Parameter Uncertainties ◽  
Computational Burden ◽  
Discrete Time Systems ◽  
Delay Dependent ◽  
Time Systems ◽  
Delay Dependent Stability ◽  
Selection Of

This paper considers the problem of global asymptotic stability of a class of uncertain discrete-time systems under the influence of finite wordlength nonlinearities (quantization and/or overflow) and time-varying delays. The parameter uncertainties are assumed to be norm-bounded. Utilizing the concept of a Wirtinger-based inequality and a reciprocally convex method, two delay-dependent stability criteria are presented. The selection of the criteria depends on the type of the nonlinearities, that is, a combination of quantization and overflow or saturation overflow nonlinearities involved in the present systems. The approach presented in this paper yields less conservative results and reduces the computational burden as compared to previously reported criteria. Numerical examples are given to illustrate the effectiveness of the presented approach.

scholarly journals Stability Criteria for Uncertain Discrete-Time Systems under the Influence of Saturation Nonlinearities and Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Siva Kumar Tadepalli ◽  
V. Krishna Rao Kandanvli ◽  
Haranath Kar
Keyword(s):  
Discrete Time ◽  
Time Varying ◽  
Stability Criteria ◽  
Time Varying Delay ◽  
Discrete Time Systems ◽  
Forward Difference ◽  
Delay Dependent ◽  
Time Systems ◽  
Delay Dependent Stability ◽  
Varying Delay

The problem of global asymptotic stability of a class of uncertain discrete-time systems in the presence of saturation nonlinearities and interval-like time-varying delay in the state is considered. The uncertainties associated with the system parameters are assumed to be deterministic and normbounded. The objective of the paper is to propose stability criteria having considerably smaller numerical complexity. Two new delay-dependent stability criteria are derived by estimating the forward difference of the Lyapunov functional using the concept of reciprocal convexity and method of scale inequality, respectively. The presented criteria are compared with a previously reported criterion. A numerical example is provided to illustrate the effectiveness of the presented criteria.

Delay-dependent stability criterion for uncertain discrete time systems in presence of actuator saturation

2017 ◽  
Vol 40 (6) ◽  
pp. 1873-1891 ◽  
Author(s):  
Vipin Chandra Pal ◽  
Richa Negi
Keyword(s):  
Discrete Time ◽  
Controller Design ◽  
Actuator Saturation ◽  
External Disturbance ◽  
Linear Matrix ◽  
Time Varying Delay ◽  
Discrete Time Systems ◽  
The Stability ◽  
Delay Dependent ◽  
Time Systems

In this paper, the idea of triple Lyapunov functional is applied for controller design of discrete time systems subjected to various nonlinearities like actuator saturation, time varying delay and uncertainties. The performance of the system considered has been examined using H∞ technique in presence of external disturbance. A novel augmented triple Lyapunov-Krasovskii functional is applied with reciprocal convex approach to achieve the stability conditions, which are based on Linear Matrix Inequality. Saturation nonlinearity is tackled using less conservative convex hull method. Numerical examples are provided to illustrate the effectiveness of the proposed criterion.

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