Gain-scheduled synthesis with dynamic positive real multipliers

Abstract

If designing robust controllers based on multiplier or separation techniques, one is confronted with weighting filters that are not necessarily stable. For optimal synthesis, this requires controllers to be only partially internally stabilizing. In this paper we propose a new synthesis framework for possibly unstable performance weights. It is further shown how these results can be used to design gain-scheduling controllers with dynamic positive real multipliers by convex optimization, a problem without any analogous solution in the literature.

Robustness analysis of linear parameter varying systems using integral quadratic constraints

“…The results in this paper also complement the recent robust performance results obtained for LPV systems whose state matrices have rational dependence on the scheduling parameters [12], [13], [14], [15]. In contrast to [12], [13], [14], [15], an arbitrary dependence on the parameters is assumed in this work and a finite-dimensional approximation based approach is taken. As noted above, this will enable applications to systems, e.g.…”

“…The robust performance analysis conditions can thus be viewed as generalizations of those given for nominal (not-uncertain) LPV systems in [4], [5]. The results in this paper also complement the recent robust performance results obtained for LPV systems whose state matrices have rational dependence on the scheduling parameters [12], [13], [14], [15]. In contrast to [12], [13], [14], [15], an arbitrary dependence on the parameters is assumed in this work and a finite-dimensional approximation based approach is taken.…”

Robustness analysis of linear parameter varying systems using integral quadratic constraints

“…It is also important to place the results of this paper in the context of existing results that use IQCs to analyze the performance of uncertain LPV systems. Specifically, there are several recent robust performance results obtained for LPV systems whose state matrices have rational dependence on the scheduling parameters [11][12][13]. In contrast to [11][12][13], the results in this paper are for the class of LPV systems whose state matrices have an arbitrary dependence on the parameters.…”

“…Specifically, there are several recent robust performance results obtained for LPV systems whose state matrices have rational dependence on the scheduling parameters [11][12][13]. In contrast to [11][12][13], the results in this paper are for the class of LPV systems whose state matrices have an arbitrary dependence on the parameters. As noted earlier, the results in this paper enable applications to systems, for example, aeroelastic vehicles or wind turbines, for which arbitrary dependence on scheduling variables is a natural modeling framework.…”