LMIs in Control/Click here to continue/Integral Quadratic Constraints/Quadratic Stability and IQCs
The System
[edit | edit source]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 | edit source]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 | edit source]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 | edit source]If there exists a such that
then the system given by is quadratically stable.
References
[edit | edit source]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