Robustness Analysis of Uncertain Time-Varying Interconnected Systems Using Integral Quadratic Constraints

Robustness analysis of uncertain time‐varying systems with unknown initial conditions

“…10,11 For instance, dissipativity-based robustness analysis results have been developed for discrete-time LTV systems, 12,31 continuous-time finite horizon LTV systems, 32,33 and interconnected discrete-time LTV systems. 34 This work falls under the class of papers that use dissipativity-based arguments for IQC-based robust stability and performance analysis and deals with discrete-time eventually periodic nominal systems, which include both finite horizon and periodic systems as special cases, subject to structured uncertainties (which could include static and dynamic, time-invariant and time-varying, linear perturbations) and potentially multiple constraints on the initial values of the state variables. The results can be viewed as an extension of the analysis result in Reference 6, which is restricted to parametric uncertainties and an unknown initial condition, and are supplementary to those developed in References 12,31.…”

“…There has also been considerable work recently on developing IQC‐based robustness analysis tools for time‐varying systems using dissipativity‐based arguments 10,11 . For instance, dissipativity‐based robustness analysis results have been developed for discrete‐time LTV systems, 12,31 continuous‐time finite horizon LTV systems, 32,33 and interconnected discrete‐time LTV systems 34 . This work falls under the class of papers that use dissipativity‐based arguments for IQC‐based robust stability and performance analysis and deals with discrete‐time eventually periodic nominal systems, which include both finite horizon and periodic systems as special cases, subject to structured uncertainties (which could include static and dynamic, time‐invariant and time‐varying, linear perturbations) and potentially multiple constraints on the initial values of the state variables.…”

Robustness analysis of uncertain time‐varying systems using integral quadratic constraints with time‐varying multipliers

“…IQC‐based dissipativity arguments differ from the homotopy arguments by employing a time‐domain, state‐space characterization of the nominal system and multipliers, thereby allowing for the extension of the results to more general classes of nominal systems and multipliers. For instance, this approach has been extended to uncertain systems in which the nominal system is an LTV system, 21 a linear parameter‐varying system, 22 and an interconnection of LTV subsystems 23 . These extensions are pushed further out by allowing the use of periodic time‐varying IQC multipliers in dissipativity results 24 …”