LMIs in Control/Click here to continue/Integral Quadratic Constraints/Frequency Domain

The System We will consider the following feedback interconnection : where and are exogeneous inputs. and are two casual operators. The Problem Let be a measurable Hermitian-valued function, and be a bounded casual operator. such that Then the feedback interconnection of and is stable. The Data is 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 If there exists a matrix such that then the feedback interconnection is 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: