5B5744 Input/Output Stability and Integral Quadratic Constraints, 3 p, spring 2000
Examiner and lecturer
room 3725, Lindstedtsv. 25, phone. 790 84 50.
In this course we discuss the operator approach to
systems analysis. The emphasis is on the integral quadratic
constraints approach to stability analysis. This approach to systems
analysis unifies the classical small gain theorem and the passivity
theorem in a nice way. We also discuss
modeling and analysis of uncertain systems, robust stability and
robust performance analysis.
The S-procedure lossless theorem is also proved and its use for
obtaining necessary conditions for robust stability and performance
Another topic is the Kalman-Yakubovich-Popov lemma (KYP) and its use for
computation in robust systems analysis. The
complete formulation of the KYP lemma is perhaps the single most
important result in control theory. The result states the equivalence
between a general LQ optimal control problem, a matrix Riccati
equation, a condition on the the eigenvalues of an Hamiltonian matrix,
a certain frequency domain Linear Matrix Inequality (LMI), and a
Finally, we discuss how the theory can be applied to practical
examples using the IQCbeta software.
- Lecturenotes [ps].
- System Analysis via Integral Quadratic Constraints by
A. Megretski and A. Rantzer.
IEEE Transactions on Automatic Control, 42(6), 1997.
Feedback Systems:Input-Output Properties, by C.A. Desoer and
Last modified: August 16, 2001 by Ulf Jönsson,