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Controllability of second order discrete-time descriptor systems

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS 2025年 31卷

作者： Phi, Ha Thuan, Do Duc Hanoi Univ Sci & Technol Fac Math & Informat 1 Dai Co Viet Str Hanoi Vietnam

This paper is mainly devoted to the controllability of second order discrete-time descriptor systems. Characterizations for different controllability concepts are derived and feedback designs are investigated by transforming the system into an appropriate form and then making use of novel methods. It shows how classical rank conditions for first order systems can be generalized to second order systems. This work extends and complements the researches about controllability of high-order descriptor systems.

关键词： Second order systems descriptor systems causal controllability complete controllability strong controllability feedback

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Impulse minimization, index reduction, and column regularization for descriptor systems

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JOURNAL OF THE FRANKLIN INSTITUTE 2025年第2期362卷

作者： Kumar, Abhinav Gupta, Mahendra Kumar Indian Inst Technol Dept Chem Engn Mumbai 400076 Maharashtra India Indian Inst Technol Bhubaneswar Dept Math Khordha 752050 Odisha India

Index of a descriptor system reflects the intensity of impulses in its solutions. The necessary and sufficient condition on descriptor systems having index at most a specific value and column regularity are established. Additionally, a necessary condition is proposed for the existence of an output feedback that can reduce the index of the system to a pre-assigned desired value while simultaneously column-regularizing the system. Furthermore, the necessary and sufficient condition is derived for the existence of an output feedback that can reduce the system's index to at most two. All theoretical conditions are proposed directly in terms of system matrices. Orthogonal transformations are used for design procedure and proofs. Numerical and physical examples are presented to support the outcome of this paper.

关键词： descriptor systems Impulse elimination Regularization Feedback design Index

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Structure-preserving linear quadratic Gaussian balanced truncation for port-Hamiltonian descriptor systems

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LINEAR ALGEBRA AND ITS APPLICATIONS 2025年 704卷 146-191页

作者： Breiten, Tobias Schulze, Philipp Tech Univ Berlin Inst Math Str 17 Juni 136 D-10623 Berlin Germany

We present a new balancing-based structure-preserving model reduction technique for linear port-Hamiltonian descriptor systems. The proposed method relies on a modification of a set of two dual generalized algebraic Riccati equations that arise in the context of linear quadratic Gaussian balanced truncation for differential algebraic systems. We derive an a priori error bound with respect to a right coprime factorization of the underlying transfer function thereby allowing for an estimate with respect to the gap metric. We further theoretically and numerically analyze the influence of the Hamiltonian and a change thereof, respectively. With regard to this change of the Hamiltonian, we provide a novel procedure that is based on a recently introduced Kalman-Yakubovich-Popov inequality for descriptor systems. Numerical examples demonstrate how the quality of reduced- order models can significantly be improved by first computing an extremal solution to this inequality. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// *** /licenses /by /4 .0/).

关键词： Port-Hamiltonian systems Model order reduction LQG control design Error bounds descriptor systems

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Robust State Feedback Control With D-Admissible Assurance for descriptor systems Subjected to Perturbed Derivative Matrix

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IEEE ACCESS 2024年 12卷 140748-140760页

作者： Huang, Chih-Peng Univ Taipei Dept Comp Sci Taipei City 100 Taiwan

This work mainly addresses the state feedback control with D-admissible assurance for descriptor systems subjected to perturbed derivative and systems' matrices simultaneously. By the linear matrix inequality (LMI) and matrix algebra manipulation, extended admissible and D-admissible analysis criteria are first presented for the regarded systems. The distinct results introduce a set of slack matrices for reducing the conservatism of the analyzing criteria, and a numerical example is given for demonstration. By involving the state feedback control, the controller design scheme can be performed for admissible and D-admissible assurance of the closed system. Since all the conditions can be formed in terms of the strict LMIs, existing LMI tools are proper for evaluation. Finally, two design examples, a numerical example and an extended RLC circuit paradigm, illustrate the validation and feasibility of the results.

关键词： Linear matrix inequalities Uncertainty State feedback Matrices Symmetric matrices PD control RLC circuits Feedback control descriptor systems state feedback control D-admissibility pole assignment linear matrix inequalities (LMIs)

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On Strict Causality Conditions for descriptor systems With Unknown Inputs

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IEEE ACCESS 2024年 12卷 195544-195551页

作者： Paitandi, Mamoni Gupta, Mahendra Kumar Natl Inst Technol Jamshedpur Dept Math Jamshedpur 831014 Jharkhand India Indian Inst Technol Bhubaneswar Dept Math Khordha 752050 Odisha India

This article investigates descriptor systems with unknown inputs that are not necessarily regular. The concept of strict causality is introduced to address the impulsive behavior of the system caused by unknown inputs and differentiating control inputs. By applying a decomposition, a reduced system is obtained, from which the unknown inputs are subsequently eliminated. Initially, conditions for causality and strict causality are presented in terms of the coefficient matrices of the reduced systems, both with and without unknown inputs. Using the strict causality of the reduced system, the strict causality condition of the original system is derived. The process to obtain these conditions is based on numerically stable orthogonal transformations. The proposed theory is elaborated with two numerical examples, demonstrating the practical relevance of the approach.

关键词： Cause effect analysis Matrix decomposition Mathematical models Indexes Vectors Trajectory Control systems Transforms Terminology systems modeling Causality differential-algebraic equations (DAEs) descriptor systems impulses strict causality unknown inputs

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Normalized P-D and Intermittent Hybrid H∞ Control for Delayed descriptor systems via Impulsive-Inputs-Dependent Conditions

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IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING 2024年 22卷 3125-3134页

作者： Zhuang, Guangming Liu, Yiqun Xia, Jianwei Xie, Xiangpeng Liaocheng Univ Sch Math Sci Liaocheng 252059 Peoples R China Nanjing Univ Posts & Telecommun Sch Internet Things Nanjing 210023 Peoples R China

The problem of normalized proportional-derivative(P-D) and intermittent hybrid H(infinity )control for delayed descriptor impulsive systems (DDISs) is studied in this work. The P-D and intermittent hybrid state feedback controller is designed, such that normalisation and H-infinity stabilisation of DDISs can be realised. A novel impulsive-inputs-dependent Lyapunov-Krasovskii functional based on a couple of auxiliary functions is constructed, which is continuous along the system state trajectories with out imposing additional conditions on impulsive dynamics. Improved H-infinity stability criterion is proposed in the form of linear matrix inequalities by utilizing free weighting matrix technique, and the H-infinity stability criterion is described as a single condition based ona combination of discrete and continuous dynamics. Finally, the usefulness of the method set forth in this work is demonstrated by a two-loop circuit network. Note to Practitioners-This work is motivated by realizingnormalized P-D and intermittent hybridH infinity control for delayeddescriptor impulsive systems. In practical engineering, manydynamic systems have to be formulated as descriptor systemswhen modeling, such as circuit systems, vehicle suspensionsystems, and so on. It is worth pointing out that infinite dynamicmodes will occur due to the algebraic constraints in descriptorsystems, and can lead to internal impulsive behavior. At the sametime, these systems are often accompanied by external impulsiveperturbations, such as the sudden failure of a component incircuit systems, etc. The internal and external impulses can causeserious damage to the system performances and stability. Mostof the existing control schemes are not well suited for suchpractical systems. In addition, due to the presence of time-varyingdelays, the delayed dynamic systems can easily collapse and cause significant damages. In this work, the P-D and intermittenthybridH infinity controller is designed so as to deal wit

关键词： Normalisation P-D and intermittent hybrid H-infinity control descriptor systems free weighting matrix time-varying delays

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Prescribed-time observer for descriptor systems with unknown input☆

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AUTOMATICA 2025年 172卷

作者： Zhang, Jiancheng Song, Yongduan Zheng, Gang Guangxi Minzu Univ Sch Math & Phys Nanning 530006 Peoples R China Guangxi Minzu Univ Ctr Appl Math Guangxi Nanning 530006 Peoples R China Chongqing Univ Sch Automat Chongqing 400044 Peoples R China Univ Lille Inria CNRS Cent LilleUMR 9189CRIStAL F-59000 Lille France

This paper investigates the problem of simultaneous state and unknown input estimation/observation within a prescribed time for a class of descriptor systems with unknown inputs (UIs). Firstly, for the descriptor system with UIs, a new structure decomposition is developed which provides a more straightforward way to estimate the state and UIs. Subsequently, based on the sub-system obtained by the decomposition, new prescribed time unknown input observers (PTUIOs) are developed for both the single-output and the multiple-output cases, which, on the one hand, achieves the simultaneous state and UI estimation within an arbitrarily prescribed time, and on the other hand, breaks through the restriction imposed in the literature that the sub-system should be single-output and meanwhile be in a special canonical form. The necessary and sufficient conditions for the existence of the PTUIO are established in terms of the original system matrices. Finally, two examples are presented to verify the effectiveness of the proposed method. (c) 2024 Published by Elsevier Ltd.

关键词： descriptor systems Prescribed-time observers Fault estimation Existence conditions

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Line zonotopes: A tool for state estimation and fault diagnosis of unbounded and descriptor systems

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AUTOMATICA 2025年 179卷

作者： Rego, Brenner S. Raimondo, Davide M. Raffo, Guilherme, V Univ Sao Paulo Dept Elect & Comp Engn BR-13566590 Sao Carlos SP Brazil Univ Trieste Dept Engn & Architecture I-34127 Trieste Italy Univ Fed Minas Gerais Dept Elect Engn BR-31270901 Belo Horizonte MG Brazil

This paper proposes new methods for set-based state estimation and active fault diagnosis (AFD) of linear descriptor systems (LDS). Unlike intervals, ellipsoids, and zonotopes, constrained zonotopes (CZs) can directly incorporate linear static constraints on state variables - typical of descriptor systems - into their mathematical representation, leading to less conservative enclosures. However, for LDS that are unstable or not fully observable, a bounded representation cannot ensure a valid enclosure of the states over time. To address this limitation, we introduce line zonotopes, a new representation for unbounded sets that retains key properties of CZs, including polynomial time complexity reduction methods, while enabling the description of strips, hyperplanes, and the entire n-dimensional Euclidean space. This extension not only generalizes the use of CZs to unbounded settings but can also enhance set-based estimation and AFD in both stable and unstable scenarios. Additionally, we extend the AFD method for LDS from Rego et al. (2020) to operate over reachable tubes rather than solely on the reachable set at the final time of the considered horizon. This reduces conservatism in input separation and enables more accurate fault diagnosis based on the entire output sequence. The advantages of the proposed methods over existing CZ-based approaches are demonstrated through numerical examples. (c) 2025 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

关键词： descriptor systems Set-based computing State estimation Fault diagnosis

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Fusion filtering for rectangular descriptor systems with stochastic bias and random observation delays under weighted try-once-discard protocol

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COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION 2024年 128卷

作者： Hu, Jun Luo, Ruonan Chen, Cai Du, Junhua Yi, Xiaojian Harbin Univ Sci & Technol Dept Appl Math Harbin 150080 Peoples R China Harbin Univ Sci & Technol Heilongjiang Prov Key Lab Optimizat Control & Inte Harbin 150080 Peoples R China Harbin Univ Sci & Technol Sch Automat Harbin 150080 Peoples R China Qiqihar Univ Coll Sci Qiqihar 161006 Peoples R China Beijing Inst Technol Sch Mechatron Engn Beijing 100081 Peoples R China Beijing Inst Technol Yangtze Delta Reg Acad Jiaxing 314003 Peoples R China Beijing Inst Technol Tangshan Res Inst Tangshan 063099 Peoples R China

This paper studies the fusion filtering problem for a class of multi-sensor rectangular descriptor systems with stochastic bias and random observation delays under weighted try-once-discard (WTOD) protocol. In order to reflect the stochastic behavior generated by disturbances, a dynamic equation is utilized to describe the stochastic bias. The random observation delays are modeled by Bernoulli random variables with individual occurrence probability. Furthermore, the WTOD protocol is used to lessen the network traffic burden. Firstly, by introducing matrix transformation and the singular value decomposition method, the rectangular descriptor systems are transformed into two non-descriptor subsystems with lower orders, where the augmentation technique is adopted to obtain new augmented systems. Secondly, the relevant local filter gains are obtained by minimizing the filtering error covariances based on the local filters (LFs) designed by new systems. Subsequently, the local filters and the fusion filters of the original descriptor systems are obtained by state transformation and covariance intersection (CI) fusion technique, respectively. The major contribution lies in that a novel fusion filtering algorithm avoiding the calculation of error cross-covariances is proposed for rectangular descriptor systems, where special effort is devoted to handling the impacts from the WTOD protocol, stochastic bias and random observation delays. Finally, the effectiveness of the fusion algorithm is demonstrated by a simulation example.

关键词： descriptor systems Covariance intersection fusion Stochastic bias Random observation delays Weighted try-once-discard protocol

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Model Predictive Control of descriptor systems

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IEEE CONTROL systems LETTERS 2024年 8卷 2139-2144页

作者： Nosrati, Komeil Belikov, Juri Tepljakov, Aleksei Petlenkov, Eduard Tallinn Univ Technol Dept Comp Syst EE-12618 Tallinn Estonia Tallinn Univ Technol Dept Software Sci EE-12618 Tallinn Estonia

While model predictive control (MPC) is widely used in the process industry for its ability to handle constraints and address complex dynamics, its conventional formulations often encounter challenges when dealing with descriptor systems. These formulations rely on system transformations that are applicable only to regular systems in specific scenarios, along with additional index assumptions. This letter formulates the MPC problem of discrete-time linear descriptor systems directly in their original state-space representation. Using the penalized weighted least-squares approach, we derive a quadratic cost function subject to the descriptor system over a finite prediction horizon. Through backward dynamic programming within each horizon, we then solve the constrained optimization problem to construct control inputs for forward-shifted prediction horizons. To accomplish this, we deal with the convergence and stability analysis of the proposed algorithm. Numerical simulations demonstrate its effectiveness compared to traditional techniques, alleviating the need for regularity and index assumptions.

关键词： Indexes Predictive control Prediction algorithms Power system stability Heuristic algorithms Cost function Vectors Discrete time predictive control optimal control descriptor systems power system

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