LMIs in Control/Click here to continue/Integral Quadratic Constraints/Frequency Domain
The System
editWe will consider the following feedback interconnection :
where and are exogeneous inputs. and are two casual operators.
The Problem
editLet be a measurable Hermitian-valued function, and be a bounded casual operator. such that
Then the feedback interconnection of and is stable.
The Data
editis a linear time-invariant system with the state space realization:
where is the state.
Any can be factorized as where and . Denote the state space realization of by .
A state space realization for the system is
The LMI
editIf there exists a matrix such that
then the feedback interconnection is stable.
References
editA. Megretski and A. Rantzer, "System analysis via integral quadratic constraints," in IEEE Transactions on Automatic Control, vol. 42, no. 6, pp. 819-830, June 1997, doi: 10.1109/9.587335
P. Seiler, "Stability Analysis With Dissipation Inequalities and Integral Quadratic Constraints," in IEEE Transactions on Automatic Control, vol. 60, no. 6, pp. 1704-1709, June 2015, doi: 10.1109/TAC.2014.2361004