IQC-synthesis with general dynamic multipliers

Abstract

SUMMARYAnalogously to the existing μ‐synthesis tools, we propose an alternative algorithm for the systematic design of robust controllers based on an iteration of standard nominal controller synthesis and integral quadratic constraint (IQC) analysis with general dynamic multipliers. The suggested algorithm enables us to perform robust controller synthesis for a significantly larger class of uncertainties if compared with the existing methods. Indeed, while the classical approaches are restricted to the use of real/complex time invariant or arbitrarily fast time‐varying parametric uncertainties, the IQC framework also offers, for example, the possibility to efficiently handle sector‐bounded and slope restricted nonlinearities or time‐varying parametric uncertainties and uncertain time‐varying time‐delays, both with bounds on the rate‐of‐variation. Secondly, in contrast to the classical approaches, the proposed techniques completely avoid gridding and curve‐fitting. We present new insights that allow us to reformulate the robust IQC analysis LMIs into a standard quadratic performance problem. This enables us to generate suitable initial conditions for each subsequent iteration step. Depending on the size of the problem, this can significantly speed up the synthesis process. The results are illustrated by means of two numerical examples. Copyright © 2013 John Wiley & Sons, Ltd.

Robust stability analysis based on finite impulse response scaling for discrete‐time linear time‐invariant systems

“…Fortunately, however, a solution to this issue has been provided in [24], in which a coupling condition is introduced between the two Lyapunov matrices in the associated inequality conditions for controller synthesis. On the basis of this result, Veenman and Scherer [25] has studied robust controller synthesis exploiting dynamic scaling. Even though these studies deal only with the continuous-time case, our discrete-time FIR scaling could also be exploited for controller synthesis, provided that a similar fundamental technique is established in the discrete-time case.…”

“…We can readily see that this leads to the realisation (25). Furthermore, we can easily see that it is reachable and observable, and thus is minimal.…”

Computation of worst-case spacing errors of vehicle platoons based on a skew-μ method∗∗This paper was supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences.

“…Veenman and Scherer (2014) suggested the following multiplier factorization in case of real uncertainty. Let the factorization matrices Φ and P have the following structure…”

“…With this multiplier factorization the following KYP lemma (Veenman and Scherer (2014)[Thm. 1]) is applicable.…”

Nonlinear robust state feedback control system design for nonlinear uncertain systems

“…The work in considers IQCs with dynamic multipliers to obtain a guaranteed cost controller, and the work in also considers the use of dynamic multipliers. The approach of uses an Linear matrix inequalities (LMI) framework for the IQCs and converts the problem into a standard quadratic performance problem. In this paper, we use the minimax linear quadratic regulator (LQR) methodology along with a structured uncertainty representation to handle the system performance and measurement feedback issues.…”