On the existence of a common quadratic Lyapunov function for two stable second order LTI discrete-time systems

2001 ◽  
Author(s):  
M. Akar ◽  
K.S. Narendra
Keyword(s):  
Lyapunov Function ◽  
Discrete Time ◽  
Second Order ◽  
Quadratic Lyapunov Function ◽  
Discrete Time Systems ◽  
Time Systems

scholarly journals On Homogeneous Parameter-Dependent Quadratic Lyapunov Function for RobustH∞Filtering Design in Switched Linear Discrete-Time Systems with Polytopic Uncertainties

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Guochen Pang ◽  
Kanjian Zhang
Keyword(s):  
Lyapunov Function ◽  
Discrete Time ◽  
Filter Design ◽  
Linear Filter ◽  
Quadratic Lyapunov Function ◽  
Discrete Time Systems ◽  
Arbitrary Switching ◽  
Polytopic Uncertainties ◽  
Parameter Dependent ◽  
Time Systems

This paper is concerned with the problem of robustH∞filter design for switched linear discrete-time systems with polytopic uncertainties. The condition of being robustly asymptotically stable for uncertain switched system and less conservativeH∞noise-attenuation level bounds are obtained by homogeneous parameter-dependent quadratic Lyapunov function. Moreover, a more feasible and effective method against the variations of uncertain parameter robust switched linear filter is designed under the given arbitrary switching signal. Lastly, simulation results are used to illustrate the effectiveness of our method.

Delay partitioning approach to the robust stability of discrete-time systems with finite wordlength nonlinearities and time-varying delays

2020 ◽  
pp. 014233122094756
Author(s):  
Kalpana Singh ◽  
V Krishna Rao Kandanvli ◽  
Haranath Kar
Keyword(s):  
Lyapunov Function ◽  
Robust Stability ◽  
Discrete Time ◽  
Time Varying ◽  
Delay Bound ◽  
Discrete Time Systems ◽  
Forward Difference ◽  
Convex Inequality ◽  
Time Systems ◽  
Delay Partitioning

This paper is associated with the problem of robust stability of discrete-time systems with time-varying delays and finite wordlength nonlinearities. The main contribution of the paper is two-fold. First, this paper presents a new Lyapunov function based on the idea of partitioning the delay interval into subintervals. The approach may be considered as an advancement over the several existing approaches where only the lower delay bound is partitioned. The second is that reciprocally convex inequality (RCI) and Wirtinger-based inequality (WBI) are used to estimate the sum terms involved in the forward difference of Lyapunov function. The intermediate delay is also included in the Lyapunov function to deal with the delay information more effectively. Finally, several examples are provided to illustrate the less conservatism of the proposed approach as compared to several existing results.

scholarly journals Partitioning Technique for Relaxed Stability Criteria of Discrete-Time Systems with Interval Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Kuang-Yow Lian ◽  
Wen-Tsung Yang ◽  
Peter Liu
Keyword(s):  
Lyapunov Function ◽  
Discrete Time ◽  
Time Varying ◽  
Stability Criteria ◽  
Discrete Time System ◽  
Interval Time ◽  
Time Varying Delay ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Varying Delay

We demonstrate an improved stability analysis based on a partition oriented technique for discrete-time systems with interval time-varying delay. The partition oriented technique introduces beneficial terms contributing to the negative definiteness of the Lyapunov function difference, meanwhile completely avoiding traditional inequality based approaches. In contrast, nonpartitioning oriented techniques do not put emphasis on further dividing the interval of the summation in the Lyapunov function. Herein, we demonstrate that the advantages of exploiting partitioning techniques manifest the relaxed stability criteria, as well as the flexibility to tune tradeoff between allowable timedelay range performance and computational load. Simulation carried out on a benchmark discrete-time system reveals the significant improvement in terms of maximum allowable upper bound in comparison.

scholarly journals Submartingales and stochastic stability

1974 ◽  
Vol 10 (2) ◽  
pp. 271-276
Author(s):  
Phil Diamond
Keyword(s):  
Lyapunov Function ◽  
Discrete Time ◽  
Stochastic Stability ◽  
Sufficient Conditions ◽  
Discrete Time Systems ◽  
Time Systems

Sufficient conditions, involving the existence of a Lyapunov function which is a submartingale of special type, are given for the instability of stochastic discrete time systems.

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