Stability analysis of weighted multiple model adaptive control of a linear time-invariant discrete-time system

2012 ◽  
Author(s):  
Weicun Zhang ◽  
Qing Li ◽  
Xiong Luo ◽  
Tao Feng
Keyword(s):  
Adaptive Control ◽  
Stability Analysis ◽  
Discrete Time ◽  
Linear Time ◽  
Multiple Model ◽  
Discrete Time System ◽  
Time System ◽  
Linear Time Invariant ◽  
Multiple Model Adaptive Control ◽  
Time Invariant

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.

scholarly journals On the Properties of Reachability, Observability, Controllability, and Constructibility of Discrete-Time Positive Time-Invariant Linear Systems with Aperiodic Choice of the Sampling Instants

2007 ◽  
Vol 2007 ◽  
pp. 1-23 ◽  
Author(s):  
M. De la Sen
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Linear Time ◽  
Time System ◽  
Linear Time Invariant ◽  
The Matrix ◽  
Metzler Matrix ◽  
Time Invariant ◽  
Time Systems ◽  
Continuous Time System

This paper investigates the properties of reachability, observability, controllability, and constructibility of positive discrete-time linear time-invariant dynamic systems when the sampling instants are chosen aperiodically. Reachability and observability hold if and only if a relevant matrix defining each of those properties is monomial for the set of chosen sampling instants provided that the continuous-time system is positive. Controllability and constructibility hold globally only asymptotically under close conditions to the above ones guaranteeing reachability/observability provided that the matrix of dynamics of the continuous-time system, required to be a Metzler matrix for the system's positivity, is furthermore a stability matrix while they hold in finite time only for regions excluding the zero vector of the first orthant of the state space or output space, respectively. Some related properties can be deduced for continuous-time systems and for piecewise constant discrete-time ones from the above general framework.

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