Discrete-time Singular Systems Research Articles

Solvability and Stability of Switched Discrete-time Singular Systems with the Same Switching Rules in Coefficient Matrices

The aim of this paper is to study the problem of solvability and stability for switched discrete-time linear singular (SDLS) systems with the same switching rules in coefficient matrices under Lipschitz perturbation. Firstly, we prove the unique existence of the solution, as well as describe the solution manifold. Secondly, by utilizing a Lyapunov function, we derive certain conditions that guarantee the stability of these systems. Finally, we illustrate our results with an example.

New LMI approach to [formula omitted] control of discrete-time singular systems

This article studies the problem of feedback H∞ control for discrete-time singular system. The objective is to design the controller to make the closed-loop system admissible and satisfy the specified H∞ performance. Firstly, the admissibility of the closed-loop system is analyzed via the Lyapunov function and linear matrix inequality (LMI) method, the admissibility condition of the singular system with H∞ performance is given. Then, applying a useful matrix inequality lemma, the controller design condition for discrete-time singular system is shown by a LMI. Specially, the benefit of the proposed design result is their less conservatism, the validity of the viewpoint is proposed by numeric illustrations.

Outlier-resistant distributed fusion filtering for nonlinear discrete-time singular systems under a dynamic event-triggered scheme

Outlier-resistant distributed fusion filtering for nonlinear discrete-time singular systems under a dynamic event-triggered scheme

On stability of switched discrete-time singular systems

On stability of switched discrete-time singular systems

Kalman Filter for Linear Discrete-Time Rectangular Singular Systems Considering Causality

This paper proposes a Kalman filter for linear rectangular singular discrete-time systems, where the singular matrix in the system is a rectangular matrix without full column rank. By using two different restricted equivalent transformation methods and adding the measurement equation to the state equation, the system is transformed into a square singular system satisfying regularity and observability. During this process, the causality of the system is taken into account, and multiple matrix transformations are applied accordingly. Based on these modifications, state estimation results are obtained using the Kalman filter. Finally, a numerical example is employed to demonstrate the effectiveness of our approach.

Fixed terminal time fractional optimal control problem for discrete time singular system

Fixed terminal time fractional optimal control problem for discrete time singular system

Discrete-State Decomposition Technique of Dissipativity Analysis for Discrete-Time Singular Systems With Time-Varying Delays.

This article is concerned with the problem of dissipativity for discrete-time singular systems with time-varying delays. First, the discrete-state decomposition technique is proposed after performing the restricted equivalent transformation for singular systems. To reduce the use of decision variables, the state-decomposed Lyapunov function is established based on the decomposed state vectors. Second, to obtain the condition with less conservatism, the two zero-value equations, especially concerning difference subsystems and algebraic ones, the discrete Wirtinger-based inequality and the extended reciprocally convex inequality are employed to bound the forward difference of the Lyapunov function. Then, the less conservative dissipativity criteria with lower computational complexity are obtained. Finally, simulation results are provided to demonstrate the superiority of the proposed technique.

On optimal control problem subject to fractional order discrete time singular systems

On optimal control problem subject to fractional order discrete time singular systems

Energy-to-Peak Controller Design for Discrete-Time Singular System

Energy-to-Peak Controller Design for Discrete-Time Singular System

Admissibility Analysis and Control for Discrete-Time Singular Systems with Interval Time-Varying Delay

This paper mainly investigates an admissibility analysis and controller design problem for an uncertain discrete-time singular system with delayed states. The time-varying delay is within an interval whose lower bound may be greater than zero. Using a modified finite sum inequality and choosing a suitable Lyapunov-Krasovskii function, we derive a set of LMI-based sufficient delay-dependent conditions for the admissibility analysis and controller synthesis problem, respectively. In the end, a numerical example shows the effectiveness and validity of the proposed approach.

Robust preview control of nonlinear uncertain discrete-time time-delayed singular systems via sliding mode approach

This paper addresses the problem of preview sliding mode control for a class of nonlinear uncertain discrete-time singular systems with time-delays. A difference operator approach is used to deal with the controlled system such that the derived augmented systems including preview information of reference signal can be constructed. A suitable surface is proposed in the sense of admissibility by the free-weighed matrix technique. Based on this, a sliding mode controller with preview information is constructed incorporating with the tracking error to ensure that the closed-loop control system reaches the designed sliding mode surface within finite time. To apply the proposed control scheme to the practical engineering systems, the sliding mode tracking controller with preview information is developed for a DC motor based on the proposed control approach. The comparative experiment results demonstrate that the preview information of reference signal can improve the tracking performance.

New Admissibility and Admissibilization Criteria for Nonlinear Discrete-Time Singular Systems by Switched Fuzzy Models

Admissibility analysis and control synthesis for nonlinear discrete-time singular systems are considered in this article. With regard to the type-1 and interval type-2 fuzzy singular systems, the partition of membership functions and scale transform is imposed, and new switched fuzzy systems, which are equivalent to the original systems, are established. A relaxed stability criterion is derived to ensure the admissibility of the system by using the piecewise Lyapunov function and singular value decomposition. Moreover, two classes of switched controllers are designed for the systems. One is for type 1 systems and the membership functions are consistent with those of the systems. The other can be applied to both of the fuzzy systems by introducing linear membership functions in each subregion. Two criteria are obtained to guarantee that the closed-loop systems are admissible. Several illustrative examples are provided to show the effectiveness of the developed methods.

Observer-based event-triggered sliding mode control of the discrete-time singular networked systems

This article is concerned with the [Formula: see text] observer-based sliding mode control via event-triggered strategy for the discrete-time singular networked systems. To improve network communication efficiency, an event-triggered strategy is introduced. Under the premise of considering the design convenience of the sliding mode surface for discrete-time singular networked systems, the observer is constructed to estimate the states of the system. From the event-triggered strategy–based observer and the sliding mode control technology, the augmented closed-loop discrete-time singular networked system is obtained. Then, new sufficient admissible criteria of discrete-time singular networked systems are derived, satisfying a given [Formula: see text] performance level. The synchronous design method of the event-triggered strategy observer gain and sliding mode control one is provided as solvable linear matrix inequalities. The sliding mode control law is designed to obtain better sliding mode accessibility and less chattering. Finally, two examples are provided to verify the effectiveness of the proposed method.

Dynamic event-triggered H∞ filtering for discrete-time singular networked control system subject to cyberattacks

This paper investigates the event-triggered filtering problem for the discrete-time singular networked control systems (DSNCS) with random cyberattacks. To more effectively utilize the limited network resource, a new dynamic event-triggered mechanism is proposed, which can effectively reduce network information transmission and save bandwidth on the premise of ensuring system performance. By considering the effect of the event-triggered mechanism and two types of cyberattacks, the filtering error system model has been constructed. Two independent random variables obeying the Bernoulli distribution are introduced to describe the two types of cyberattacks. Sufficient conditions that can guarantee the admissibility of the filtering error system have been developed with Lyapunov stability theory and LMIs techniques. Moreover, the co-design method is present in terms of LMIs to derive the parameters of dynamic event-triggered mechanism and the designed [Formula: see text] filter synchronously. Finally, an illustrative example is employed to verify the usefulness of the proposed method.

Reduced-order filtering for discrete-time singular systems under fading channels

In this paper, the reduced-order filtering problem for discrete-time singular systems under fading channels is studied. Our aim is to design a reduced-order filter to ensure the filtering error system with fading measurements is stochastically admissible and meets the given performance index. And the designed method is less conservative. However, the standard linear matrix inequality (LMI) cannot be obtained due to the nonlinear terms in decoupling. For this purpose, a new LMI is obtained by using new decoupling method. Finally, numerical example and electrical circuit example are given to clearly illustrate that the proposed method is less conservative than that of the existing method.

State bounding estimation of positive singular discrete-time systems with unbounded time-varying delays

This paper investigates the problem of state bounding for linear positive singular discrete-time systems with unbounded time-varying delay. Our approach is based on the comparison principle and the spectral analysis of matrices. Using the proposed approach, we provide new sufficient conditions for the regularity, causality, positivity and the existence of the smallest ultimate upper bound of such systems. The conditions are given in terms of linear programming problems, which can be solved by LP optimal toolbox. Numerical examples with simulation are given to demonstrate the advantage and validity of the proposed theoretical results. The proposed method is the first trial in the state bounding problem of linear singular discrete-time systems with unbounded time-varying delays.

H∞ Reliable Dynamic Output-Feedback Controller Design for Discrete-Time Singular Systems with Sensor Saturation

In this study, we investigate the H∞ fault-tolerant control problem for a discrete-time singular system which is subject to external disturbances, actuator faults, and sensor saturation. By assuming that the state variable of the system is unavailable for measurement, and the actuator fault can be described by a Markovian jump process, attention is mainly focused on designing a reliable dynamic output-feedback (DOF) controller able to compensate for the effects of the aforementioned factors on the system stability and performance. Based on the sector non-linear approach to handle the sensor saturation, a new criterion is established to ensure that the closed-loop system is stochastically admissible with a γ level of the H∞ disturbance rejection performance. The main aim of this work is to develop a procedure for synthesizing the controller gains without any model transformation or decomposition of the output matrix. Therefore, by introducing a slack variable, the H∞ admissibility criterion is successfully transformed in terms of strict linear matrix inequalities (LMIs). Three practical examples are exploited to test the feasibility and effectiveness of the proposed approach.

Peak-to-Peak Filtering for Discrete-Time Singular Systems

This brief on peak-to-peak filtering is carried out for discrete-time singular systems in this brief. For the sake of designing the required filter, it makes the filtering error system admissible (regular, causal, and stable), meanwhile, preserves the specified peak-to-peak performance level. By introducing a novel Lyapunov function, the peak-to-peak performance of the filtering error system is analyzed on the strength of matrix inequalities. Then, based on linear matrix inequalities (LMIs), significant design conditions of the peak-to-peak filter for discrete-time singular systems are proposed. In the end, a RC circuit is presented to verify the availability of the results.

Robust finite-time sliding mode control for discrete-time singular system with time-varying delays

This paper explores the finite-time bounded issue for discrete-time singular time-varying delay system via sliding mode control method. A suitable discrete-time sliding mode control law is constructed to drive the state trajectories onto the specified sliding surface in a given finite time interval. Meanwhile, sufficient conditions for finite-time bounded to the closed-loop delayed system are provided in both reaching phase and sliding motion phase. In addition, the finite-time sliding mode controller gain matrix can be solved by using the linear matrix inequalities approach. Finally, three numerical examples are illustrated to demonstrate the superiority and practicability of presented results.

Observer-Based Fuzzy Controller Design for Nonlinear Discrete-Time Singular Systems via Proportional Derivative Feedback Scheme

This paper investigates the observer-based fuzzy controller design method for nonlinear discrete-time singular systems that are represented by Takagi-Sugeno (T-S) fuzzy models. At first, the nonlinearity can be well-approximated with several local linear input-output relationships. The parallel distributed compensation (PDC) technology and the proportional derivative (PD) feedback scheme are then employed to construct the observer-based fuzzy controller. To solve the problem of unmeasured states, the impulsive phenomenon of singular systems, and the PD scheme’s reasonableness, a novel observer-based fuzzy controller is developed. By using the Lyapunov theory and projection lemma, the stability criteria are built in terms of linear matrix inequalities (LMI). Moreover, the gains of fuzzy controller and fuzzy observer can be calculated synchronously by using convex optimization algorithms. Finally, a biological economic system is provided to verify the effectiveness of the proposed fuzzy control method.