LMIs in Control/Click here to continue/Integral Quadratic Constraints/Quadratic Stability and IQCs
The System edit
Consider the system of differential equations
where are given and is Hurwitz. is the set of all diagonal matrices with the norm not exceeding 1.
The Problem edit
The system is called quadratically stable if there exists a matrix such that
The stability of the system above is equivalent to the stability of the feedback interconnection:
where is the linear time-invariant operator with transfer function , and is the operator,
The Data edit
Let
where are real matrices such that
For a fixed matrix satisfying the inequality above, a sufficient condition of stability is given by
The LMI edit
If there exists a such that
then the system given by is quadratically stable.
References edit
A. 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