On the exponential stability of discrete-time systems with applications in observer design

1994 ◽  
Vol 39 (9) ◽  
pp. 1959-1962 ◽  
Author(s):  
V.C. Aitken ◽  
H.M. Schwartz
Keyword(s):  
Exponential Stability ◽  
Discrete Time ◽  
Observer Design ◽  
Discrete Time Systems ◽  
Time Systems

Observer Design for the Minimum-Time State Reconstruction of Linear Discrete-Time Systems

1979 ◽  
Vol 101 (4) ◽  
pp. 350-354 ◽  
Author(s):  
John O’Reilly
Keyword(s):  
Discrete Time ◽  
Observer Design ◽  
Minimum Time ◽  
System State ◽  
Minimal Order ◽  
State Reconstruction ◽  
Discrete Time Systems ◽  
Observability Index ◽  
Time Systems ◽  
Time Linear

The problem of observer design for the minimum-time state reconstruction of a general class of discrete-time linear multivariable systems is considered. Both full-order and minimal-order observers, each specified by a gain matrix in closed form, are presented which reconstruct the system state in a minimum of vo and vo − 1 steps respectively, where vo is the system observability index. The simplicity and generality of the designs are demonstrated by numerical example.

scholarly journals Nonuniform Exponential Trichotomy for Linear Discrete-Time Systems in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Xiao-qiu Song ◽  
Tian Yue ◽  
Dong-qing Li
Keyword(s):  
Exponential Stability ◽  
Banach Spaces ◽  
Discrete Time ◽  
Difference Equations ◽  
Exponential Dichotomy ◽  
Linear Difference Equations ◽  
Discrete Time Systems ◽  
Exponential Trichotomy ◽  
Time Systems

The aim of this paper is to give several characterizations for nonuniform exponential trichotomy properties of linear difference equations in Banach spaces. Well-known results for exponential stability and exponential dichotomy are extended to the case of nonuniform exponential trichotomy.

Exponential Stability Analysis of Fixed Point Interfered Nonlinear Digital Systems in the Presence of Quantization and Overflow Constraints

2020 ◽  
Vol 19 (04) ◽  
pp. 2050040
Author(s):  
Saddam Hussain Malik ◽  
Muhammad Tufail ◽  
Muhammad Rehan ◽  
Shakeel Ahmed
Keyword(s):  
Fixed Point ◽  
Stability Analysis ◽  
Exponential Stability ◽  
Discrete Time ◽  
Digital Systems ◽  
Discrete Time System ◽  
Time System ◽  
Discrete Time Systems ◽  
Digital Hardware ◽  
Time Systems

Finite word length is a practical limitation when discrete-time systems are implemented by using digital hardware. This restriction degrades the performance of a discrete-time system and may even lead it toward instability. This paper, addresses the stability and disturbance attenuation performance analysis of nonlinear discrete-time systems under the influence of energy-bounded external interferences when such systems are subjected to quantization and overflow effects of fixed point hardware. The proposed methodology, in comparison with previous paper, describes exponential stability for the nonlinear discrete-time systems by considering composite nonlinearities of digital hardware. The proposed criteria that ensure exponential stability and [Formula: see text] performance index for the digital systems under consideration are presented in the form of a set of linear matrix inequalities (LMIs) by exploiting Lyapunov stability theory, Lipschitz condition and sector conditions for different types of commonly used quantization and overflow arithmetic properties, and the results are validated for recurrent neural networks. Furthermore, novel stability analysis results for a nonlinear discrete-time system under hardware constraints can also be observed as a special case of the proposed criteria.

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