Robust Performance Analysis for Structured Linear Time-Varying Perturbations With Bounded Rates-of-Variation

• Published in: IEEE transactions on automatic control Vol. 52; no. 2; pp. 197 - 211
• Main Authors: Koroglu, H., Scherer, C.W.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.02.2007; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Blocking; Bounded-rate parameter variations; Computation; Computer science; control theory; systems; Control system analysis; Control theory. Systems; Distributed computing; Dynamic tests; Dynamics; Exact sciences and technology; integral quadratic constraints (IQC); Kalman-Yakubovich-Popov (KYP) lemma; linear matrix inequalities (LMI); Lower bounds; Optimization; Performance analysis; Perturbation methods; Robust control; robust performance analysis; Robust stability; Robustness; slowly time-varying systems; Stability analysis; structured uncertainty; Studies; Testing; Time varying systems; Uncertainty; Upper bound; Upper bounds; Lower bound; robust performance analysis; structured uncertainty; Semi definite programming; Linear time; linear matrix inequalities (LMI); Optimization; Robust control; Time varying system; Upper bound; Linear time invariant system; Uncertain system; Bounded-rate parameter variations; Electrical network; Diagonal matrix; Yakubovich Kalman Popov lemma; integral quadratic constraints (IQC); Linear matrix inequality; Performance analysis; Linear perturbation; slowly time-varying systems; Bounded perturbation; Kalman-Yakubovich-Popov (KYP) lemma
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2006.890482

The robust performance analysis problem is considered for linear time-invariant (LTI) systems subject to block-diagonal structured and bounded linear time-varying (LTV) perturbations with specified maximal rates-of-variation. Analysis methods are developed in terms of semidefinite programming for the computation of upper and lower bounds for the optimum robust performance level. The upper bound computation is based on an integral quadratic constraint (IQC) test developed using a generalized version of the so-called swapping lemma. The lower bound computation method employs an extended version of the power distribution theorem together with a generalized version of the Kalman-Yakubovich-Popov (KYP) lemma and serves as a means to assess the conservatism of the computed upper bounds in the case of dynamic LTV perturbations. As corollaries of the underlying result for lower bound computation, it is shown for general block-diagonal uncertainty structures that thefrequency-dependent/constant D-scaling tests are exact for robust performance analysis against arbitrarily slow/fast dynamic LTV perturbations, respectively