LMIs in Control/Stability Analysis/Discrete Time/Output Energy Bound for 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 Consider the continuous-time, LTI autonomous system with state space representation , , where and Determining an Upper Bound The output of this system will satisfy if there exists some matrix and scalar such that , , . Conclusion 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 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. Return to Main Page: