LMIs in Control/Click here to continue/LMIs in system and stability Theory/Output Energy Bound for Discrete-Time Autonomous LTI Systems
Output Energy Bound for Autonomous LTI Systems
Autonomous systems are initialized under a given set of initial conditions, and then run without any additional inputs. It is useful to know ahead of time the bounds such a system will operate within. This analysis can be used to determine the upper bound on the output of a given autonomous LTI system.
The System edit
Consider the continuous-time, LTI autonomous system with state space representation
,
,
where and
Determining an Upper Bound edit
The output of this system will satisfy
if there exists some matrix and scalar such that
,
,
.
Conclusion edit
Given an autonomous system with an initial operating condition, the parameter can be used to determine the largest feasible bound on the output of that system.
External Links edit
A list of references documenting and validating the LMI.
- LMI Methods in Optimal and Robust Control - A course on LMIs in Control by Matthew Peet.
- LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.
- LMIs in Systems and Control Theory - A downloadable book on LMIs by Stephen Boyd.