scholarly journals Minimum System Sensitivity Study of Linear Discrete Time Systems for Fault Detection

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Xiaobo Li ◽  
Hugh H. T. Liu
Keyword(s):  
Fault Detection ◽  
Riccati Equation ◽  
Discrete Time ◽  
Time Horizon ◽  
Linear Time ◽  
Sensitivity Study ◽  
Algebraic Riccati Equation ◽  
System Sensitivity ◽  
Discrete Time Systems ◽  
Time Systems

Fault detection is a critical step in the fault diagnosis of modern complex systems. An important notion in fault detection is the smallest gain of system sensitivity, denoted asℋ−index, which measures the worst fault sensitivity. This paper is concerned with characterizingℋ−index for linear discrete time systems. First, a necessary and sufficient condition on the lower bound ofℋ−index in finite time horizon for linear discrete time-varying systems is developed. It is characterized in terms of the existence of solution to a backward difference Riccati equation with an inequality constraint. The result is further extended to systems with unknown initial condition based on a modifiedℋ−index. In addition, for linear time-invariant systems in infinite time horizon, based on the definition of theℋ−index in frequency domain, a condition in terms of algebraic Riccati equation is developed. In comparison with the well-known bounded real lemma, it is found thatℋ−index is not completely dual toℋ∞norm. Finally, several numerical examples are given to illustrate the main results.

scholarly journals Optimal Robust Fault Detection for Linear Discrete Time Systems

2008 ◽  
Vol 2008 ◽  
pp. 1-16 ◽  
Author(s):  
Nike Liu ◽  
Kemin Zhou
Keyword(s):  
Fault Detection ◽  
Discrete Time ◽  
Filter Design ◽  
Algebraic Riccati Equation ◽  
Optimization Criteria ◽  
Robust Detection ◽  
Discrete Time Systems ◽  
Robust Fault Detection ◽  
Time Systems ◽  
Detection Filter

This paper considers robust fault-detection problems for linear discrete time systems. It is shown that the optimal robust detection filters for several well-recognized robust fault-detection problems, such asℋ−/ℋ∞,ℋ2/ℋ∞, andℋ∞/ℋ∞problems, are the same and can be obtained by solving a standard algebraic Riccati equation. Optimal filters are also derived for many other optimization criteria and it is shown that some well-studied and seeming-sensible optimization criteria for fault-detection filter design could lead to (optimal) but useless fault-detection filters.

Modal Control of Linear Time-Invariant Discrete-Time Systems

1969 ◽  
Vol 2 (8) ◽  
pp. T133-T136 ◽  
Author(s):  
B. Porter ◽  
T. R. Crossley
Keyword(s):  
Discrete Time ◽  
Linear Time ◽  
Feedback Loops ◽  
Modal Control ◽  
Discrete Time System ◽  
Linear Time Invariant ◽  
Modal Theory ◽  
Discrete Time Systems ◽  
Time Invariant ◽  
Time Systems

Modal control theory is applied to the design of feedback loops for linear time-invariant discrete-time systems. Modal theory is also used to demonstrate the explicit relationship which exists between the controllability of a mode of a discrete-time system and the possibility of assigning an arbitrary value to the eigenvalue of that mode.

Sign in / Sign up

Export Citation Format

Share Document