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 | edit source]
Consider the continuous-time, LTI autonomous system with state space representation
,
,
where and
Determining an Upper Bound[edit | edit source]
The output of this system will satisfy
if there exists some matrix and scalar such that
,
,
.
Conclusion[edit | edit source]
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 | edit source]
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.