This paper investigates the robust stability and stabilization analysis of interval fractional-order systems with time-varying delay. The stability problem of such systems is solved first, and then using the proposed results a stabilization theorem is also included, where sufficient conditions are obtained for designing a stabilizing controller with a predetermined order, which can be chosen to be as low as possible. Utilizing efficient lemmas, the stability and stabilization theorems are proposed in the form of LMIs, which is more suitable to check due to various existing efficient convex optimization parsers and solvers. Finally, two numerical examples have shown the effectiveness of our results.
This paper deals with the problem of robust dynamic output feedback stabilization of interval fractional-order linear time invariant (FO-LTI) systems with the fractional order $1\leα<2$. In this study, a new formulation based on the null-space analysis of the system matrices is proposed using linear matrix inequalities (LMIs). The applied uncertain model is the most complete model of linear interval systems, in which all of the systems matrices are interval matrices. A robust dynamic output feedback controller is designed that asymptotically stabilizes the interval FO-LTI system, where no limi…
This paper discusses the stability analysis of linear parameter varying systems with a parameter-dependent delay where the parameters are assumed to be stochastic piecewise constants under spontaneous Poissonian jumps. Based on stochastic Lyapunov-Krasovskii functionals, we also provide sufficient synthesis conditions for the gain-scheduled state-feedback controller with memory in terms of parameter-dependent linear matrix inequalities (LMIs). Such synthesis conditions are computationally intractable due to the presence of integral terms. However, we show that these LMIs can be equivalently re…
This paper investigates the distributed consensus tracking control problem for general linear multi-agent systems (MASs) with external disturbances and heterogeneous time-varying input and communication delays under a directed communication graph topology, containing a spanning tree. First, for all agents whose state matrix has no eigenvalues with positive real parts, a communication-delay-related observer, which is used to construct the controller, is designed for followers to estimate the leader's state information. Second, by means of the output regulation theory, the results are relaxed to…
This paper deals with the problem of providing a data-driven solution to the local stabilization of linear systems subject to input saturation. After presenting a model-based solution to this well-studied problem, a systematic method to transform model-driven into data-driven LMI conditions is presented. This technical solution is demonstrated to be equivalent to the recent advanced results on LMI formulations based on S-procedure or Peterson Lemmas. However, the advantage of the proposed method relies on its simplicity and its potential to be applicable to a wide class of problems of stabiliz…
Hyperexponential stability is investigated for dynamical systems with the use of both, explicit and implicit, Lyapunov function methods. A nonlinear hyperexponential control is designed for stabilizing linear systems. The tuning procedure is formalized in LMI form. Through numeric experiments, it is observed that the proposed hyperexponential control is less sensitive with respect to noises and discretization errors than its finite-time analog. It also demonstrates better performance in the presence of delays as well. Theoretical results are supported by numerical simulations.
This paper studies the boundary output feedback stabilization of general 1-D reaction-diffusion PDEs in the presence of a state delay in the reaction term. The control input applies through a Robin boundary condition while the system output is selected as a either Dirichlet or Neumann boundary trace. The control strategy takes the form of a finite-dimensional observer-based controller with feedback and observer gains that are computed in order to dominate the state delayed term. For any arbitrarily given value of the state delay, we show the exponential stability of the resulting closed-loop s…
ISIM1s consists of a few MATLAB functions and a script that can be used to derive stabilizing impulsive controllers for delay differential equations. This document serves as both a manual and tutorial on the functionality of the ISIM1s package. Brief background on the theoretically guaranteed stabilization scenario are provided before the primary MATLAB script is explained. The tutorial demonstrates how the package can be used to derive stabilizing impulsive controllers for delay differential equations of various complexity scales. Emphasis is placed on the role of various tuning parameters.
This paper deals with the exponential input-to-state stabilization with respect to boundary disturbances of a class of diagonal infinite-dimensional systems via delay boundary control. The considered input delays are uncertain and time-varying. The proposed control strategy consists of a constant-delay predictor feedback controller designed on a truncated finite-dimensional model capturing the unstable modes of the original infinite-dimensional system. We show that the resulting closed-loop system is exponentially input-to-state stable with fading memory of both additive boundary input perturb…
This paper addresses the boundary output feedback stabilization of general 1-D reaction-diffusion PDEs with delayed boundary measurement. The output takes the form of a either Dirichlet or Neumann trace. The output delay can be arbitrarily large. The control strategy is composed of a finite-dimensional observer that is used to observe a delayed version of the first modes of the PDE and a predictor component which is employed to obtain the control input to be applied at current time. For any given value of the output delay, we assess the stability of the resulting closed-loop system provided th…
This paper discusses the boundary feedback stabilization of a reaction-diffusion equation with Robin boundary conditions and in the presence of a time-varying state-delay. The proposed control design strategy is based on a finite-dimensional truncated model obtained via a spectral decomposition. By an adequate selection of the number of modes of the original infinite-dimensional system, we show that the design performed on the finite-dimensional truncated model achieves the exponential stabilization of the original infinite-dimensional system. In the presence of distributed disturbances, we sh…
This paper discusses the in-domain feedback stabilization of reaction-diffusion PDEs with Robin boundary conditions in the presence of an uncertain time- and spatially-varying delay in the distributed actuation. The proposed control design strategy consists of a constant-delay predictor feedback designed based on the known nominal value of the control input delay and is synthesized on a finite-dimensional truncated model capturing the unstable modes of the original infinite-dimensional system. By using a small-gain argument, we show that the resulting closed-loop system is exponentially stable…
This paper is concerned with the point torque boundary feedback stabilization of a damped Euler-Bernoulli beam model in the presence of a time-varying state-delay. First, a finite-dimensional truncated model is derived by spectral reduction. Then, for a given stabilizing state-feedback of the delay-free truncated model, an LMI-based sufficient condition on the maximum amplitude of the state-delay is employed to guarantee the stability of the closed-loop state-delayed truncated model. Second, we assess the exponential stability of the resulting closed-loop infinite-dimensional system under the …
This paper is concerned with the output feedback boundary stabilization of general 1-D reaction diffusion PDEs in the presence of an arbitrarily large input delay. We consider the cases of Dirichlet/Neumann/Robin boundary conditions for the both boundary control and boundary condition. The boundary measurement takes the form of a either Dirichlet or Neumann trace. The adopted control strategy is composed of a finite-dimensional observer estimating the first modes of the PDE coupled with a predictor to compensate the input delay. In this context, we show for any arbitrary value of the input del…
This study deals with analysis and control of cooperative synchronization for identical agents interacting on a directed graph topology. The agents are considered to have general continuous linear time-invariant dynamics with homogeneous communication and/or control delays. An LMI approach based on a Lyapunov-Krasovskii functional is proposed, together with the synchronizing region concept, which decouples the single-agent dynamics from the detailed graph topology. Moreover, the conventional notion of synchronizing region is here extended by an LMI relaxation utilizing quasi-convex characteris…
In this note, we present an effective solution to the stabilization of linear input delay systems subject to dissipative constraints while all the effect of input delay is compensated by a controller with novel structure. The method is inspired by the recent development in the mathematical treatment of distributed delays and predictor controllers, which are critical for the derivation of the solution. An important conceptual innovation is the use of a parameterized dynamical state feedback controller (DSFC), where the dimension of the controller equals the dimension of the control input. A suf…
Global Stabilization of Nonlinear Delay Systems With a Compact Absorbing Set
National Technical University of Athens（雅典国立技术大学）；University of California, San Diego（加州大学圣地亚哥分校）；Laboratoire GREYC CNRS-ENSICAEN（GREYC国家科学研究中心-ENSICAEN实验室）；Centre National de la Recherche Scientifique, CNRS-EECI SUPELEC（法国国家科学研究中心，CNRS-EECI苏佩莱克）
This paper studies the stabilization and safety problems of nonlinear time-delay systems, where time delays exist in system state and affect the controller design. Following the Razumikhin approach, we propose a novel control Lyapunov-Razumikhin function to facilitate the controller design and to achieve the stabilization objective. To ensure the safety objective, we propose a Razumikhin-type control barrier function for time-delay systems for the first time. Furthermore, the proposed Razumikhin-type control Lyapunov and barrier functions are merged such that the stabilization and safety contr…
In this paper, the model predictive control is designed for an interval type-2 Takagi-Sugeno (T-S) system with unknown time-varying delay in state and input vectors. The time-varying delay is a weird phenomenon that is appeared in almost all systems. It can make many problems and instability while the system is working. In this paper, the time-varying delay is considered in both states and input vectors and is the sensible difference between the proposed method here and previous algorithms, besides, it is unknown but bounded. To solve the problem, the Razumikhin approach is applied to the prop…
This paper presents a new method for dynamic output feedback stabilizing controller design for decomposable systems with switching topology and delay. Our approach consists of two steps. In the first step, we model the decomposable systems with switching topology as equivalent LPV systems with a piecewise constant parameter. In the second step, we design stabilizing output feedbacks for these LPV systems in the presence of a time-varying output delay using a trajectory-based stability analysis approach. We do not impose any constraint on the delay derivative. Finally, we illustrate our approac…
Robust Adaptive Sliding Mode Control of Markovian Jump Systems with Uncertain Mode-dependent Time-varying Delays and Partly Unknown Transition Probabilities
Mississippi State University（密西西比州立大学）；University of Notre Dame（圣母大学）；Arak University（阿拉克大学）；Tarbiat Modares University（塔里亚特莫达雷斯大学）
Stability Analysis and Data-Driven State Estimation for Generalized Persidskii Systems with Time Delays: Theory and Experimental Validation on PMSM Drives
College of Engineering and Physical Sciences, Khalifa University（Khalifa大学工程与物理科学学院）
In this paper, we study the application of switched systems stability criteria to derive delay-dependent conditions for systems affected by both a constant and a time-varying delay. The main novelty of our approach lies on the use of path-complete Lyapunov techniques along with the proposition of a new modified functional to obtain convex analysis conditions while avoiding the need of computing a dwell time for each mode in a switched system representation, as usual in the \textit{switched approach} for time-delay systems. Furthermore, we leverage the developed analysis to obtain LMIs for the …
This paper studies the stabilization and safety problems of nonlinear time-delay systems. Following both Razumikhin and Krasovskii approaches, we propose novel control Lyapunov functions/functionals for the stabilization problem and novel control barrier functions/functionals for the safety problem. The proposed control Lyapunov and barrier functions/functionals extend the existing ones from the delay-free case to the time-delay case, and allow for designing the stabilizing and safety controllers in closed-form. Since analytical solutions to time-delay optimal control problems are hard to be a…
