LMIs in Control/Click here to continue/Integral Quadratic Constraints/Quadratic Stability and IQCs

The System 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 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 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 If there exists a such that then the system given by is quadratically stable. References 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 Return to Main Page: