This paper develops a new control framework for linear parameter-varying (LPV) systems with time-varying state delays by integrating parameter-dependent Lyapunov functions with integral quadratic constraints (IQCs). A novel delay-dependent state-feedback controller structure is proposed, consisting of a linear state-feedback law augmented with an additional term that captures the delay-dependent dynamics of the plant. Closed-loop stability and $\mathcal{L}_2$-gain performance are analyzed using dynamic IQCs and parameter-dependent quadratic Lyapunov functions, leading to convex synthesis conditions that guarantee performance in terms of parameter-dependent linear matrix inequalities (LMIs). Unlike traditional delay control approaches, the proposed IQC-based framework provides a flexible and systematic methodology for handling delay effects, enabling enhanced control capability, reduced conservatism, and improved closed-loop performance.
Time-delay systems have received considerable attention over the past decades due to their widespread presence in practical engineering applications, including industrial manufacturing processes [15], neural networks [14,27,12], and fuzzy dynamical systems [20,6,34]. The presence of delays often induces instability and performance degradation, which has motivated the development of various tools for stability analysis and controller design [9,7,3].
Early research primarily focused on systems with constant delays, and the theory for stability and stabilization of linear time-invariant (LTI) systems with constant delays is now well established [18,13]. More recently, time-varying delays have attracted increasing attention, as they naturally arise in large-scale complex systems such as networked control systems [15,14,27,12] and underwater vehicles [16]. This has led to extensive investigations on the analysis and synthesis of systems with time-varying delays [7,19,10,4], including the development of various stability and performance criteria [19]. A common approach in these studies is the construction of Lyapunov-Krasovskii functionals (LKFs) to obtain delay-dependent analysis results. Although more sophisticated LKFs often reduce conservatism, identifying the precise sources of conservatism remains challenging, as does designing functionals that achieve a desirable balance between accuracy and computational efficiency.
A further difficulty associated with LKF-based approaches arises in control synthesis. Most synthesis conditions derived from LKFs are inherently non-convex, frequently taking the form of bilinear matrix inequalities (BMIs) due to the coupling between Lyapunov and controller decision matrices [7,3,4]. To obtain computationally tractable conditions, auxiliary variables or structural constraints are typically introduced, which inevitably introduce additional conservatism. Consequently, a persistent gap exists between analysis and synthesis results, explaining why synthesis conditions are often more conservative despite the rich body of analysis results. In the context of LPV systems, [30,29] presents an analysis and state-feedback synthesis framework for LPV systems with parameter-dependent delays. Stability and induced L 2 performance conditions are formulated as LMIs using parameter-dependent Lyapunov-Krasovskii functionals, enabling convex computation. Subsequently, [5] proposes δ-memory-resilient gain-scheduled state-feedback controllers for uncertain LTI/LPV systems, unifying memoryless and exact-memory controllers while explicitly accounting for mismatch between system and controller delays.
Integral quadratic constraints (IQCs), introduced by Megretski and Rantzer [17], provide an alternative framework for modeling nonlinearities and uncertainties, including saturation, dead zones, delays, parametric uncertainties, and unmodeled dynamics. IQCs have been successfully applied to stability analysis and stabilization of uncertain dynamical systems [3,10,11,25,26]. For time-delay systems, IQC-based methods offer several advantages over LKF-based approaches by explicitly characterizing the input-output behavior of delayed dynamics. This representation reveals the sources of conservatism more transparently and provides systematic mechanisms for reducing it. Libraries of IQC multipliers for continuous-and discrete-time LTI systems with time-varying delays have been developed [10,11], while alternative formulations include static IQCs, input-output methods [8], and quadratic separation techniques [1]. Despite these advances, nearly all existing IQC-based results for delayed systems focus primarily on stability and performance analysis, whereas control synthesis within the IQC framework has not been adequately explored. For example, [22] presents a robust LPV analysis framework that combines LPV system modeling with uncertainties described by integral quadratic constraints (IQCs)for delayed systems, providing computationally efficient conditions for assessing robust performance. The approach generalizes the nominal LPV bounded real lemma to systems whose state matrices have arbitrary dependence on time-varying parameters, extending applicability beyond prior rational-dependence methods. It also shows significant performance improvement using dynamic IQC with parameter dependent Lyapunov functions. This observation motivates the present work, which exploits the IQC methodology to address the delay control synthesis problem with both stringent performance guarantees and computational efficiency. Recent studies such as [31] introduce a dynamic IQC-based exact-memory control framework for uncertain linear systems with time-varying state delays, embedding the delay operator directly into the controller and yielding fully convex H ∞ synthesis conditions with reduced conservatism. Similarly, [32] develops a dynamic IQC-based exact-memory output-feedback control scheme for linear systems with time-varyi
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