Sampled-data Systems Research Articles

Destabilizing effect of Coulomb friction induced limit cycles on sampled-data linear systems

AbstractThis paper presents a counterintuitive effect of Coulomb friction on the dynamics of sampled-data linear systems. Due to dry friction, the motion becomes sensitive to the initial conditions, and the different possible motion trajectories are separated by limit cycles. This paper shows that the linearly stable behavior of the frictionless case degrades due to the presence of dry friction and how the stable domain of operation decreases. The results are illustrated through the example of a single-degree-of-freedom system model. The presented analysis of the nonlinear system gives insight into the intricate dynamics of sampled-data systems due to the effect of dry friction, and numerical simulations verify the results.

ℒ2-gain performance of nonlinear sampled-data systems with gain-scheduled control

This paper presents new sufficient conditions for stabilisation of sampled-data nonlinear systems, recast as quasi-linear parameter-varying models. The adopted control strategy considers gain-scheduled state-feedback controllers subject to induced input delay. The L 2 -gain performance is investigated in the sense of Lyapunov. After the proposition of a Lyapunov function and with the application of Wirtinger's inequality, the derived conditions are rewritten in terms of linear matrix inequalities. Aiming at the enlargement of the aperiodic sampling time and at the minimisation of the L 2 -gain, the effectiveness of the developed approach is assessed through numerical simulations.

Leader-Following Sampled-Data Consensus of Multiagent Systems With Successive Packet Losses and Stochastic Sampling.

In practical applications, sampled-data systems are often affected by unforeseen physical constraints that cause the sampling interval to deviate from the expected value and fluctuate according to a certain probability distribution. This probability distribution can be determined in advance through statistical analysis. Taking into account this stochastic sampling interval, this article focuses on addressing the leader-following sampled-data consensus problem for linear multiagent systems (MASs) with successive packet losses. First, the relationship of the equivalent sampling interval between two successive update instants is established, taking into account the double randomness introduced by both SPLs and stochastic sampling. Then, the equivalent discrete-time MAS is obtained, and the overall leader-following consensus problem is formulated as a stochastic stability problem of the equivalent system by incorporating the sampled-data consensus protocol and properties of the Laplacian matrix. Based on the equivalent the discrete-time system, a consensus criterion is derived under a directed graph by using the Lyapunov theory and leveraging a vectorization technique. By the introduction of a matrix reconstruction approach, the mathematical expectation of a product of three matrices, including the system matrix and its transpose, can be determined. Then, the consensus protocol gain is designed. Finally, an example is provided to validate our theoretical results.

A new quasi-finite-rank approximation of compression operators on [formula omitted] with applications to sampled-data and time-delay systems: Piecewise linear kernel approximation approach

This paper provides a new quasi-finite-rank approximation (QFRA) of infinite-rank compression operators defined on the Banach space L∞[0,H), which are associated with tractable representations of infinite-dimensional systems such as time-delay and sampled-data systems. We first formulate the QFRA by an optimization problem with a matrix-valued parameter X to minimize the associated error in terms of the L∞[0,H)-induced norm. To facilitate solving the optimization problem, we next employ the piecewise linear kernel approximation (PLKA) technique, by which the optimization problem is then converted to a linear programming (LP) problem. The solution of the LP problem is shown to converge to the optimal solution of the original QFRA with the order of 1/M, where M is the PLKA parameter. The PLKA-based QFRA is shown to lead to practical methods of the stability analysis for time-delay systems and the L1 optimal controller synthesis for sampled-data systems. Finally, the overall arguments developed in this paper are demonstrated through some numerical and experimental studies.

Asynchronous Filtering for Fuzzy Sampled-Data Systems Subject to Censored Measurements and Nonuniform Sampling

Asynchronous Filtering for Fuzzy Sampled-Data Systems Subject to Censored Measurements and Nonuniform Sampling

Deterministic learning-based neural output-feedback control for a class of nonlinear sampled-data systems

Deterministic learning-based neural output-feedback control for a class of nonlinear sampled-data systems

Stabilization of T–S fuzzy membership-function dependent H$$_\infty $$-based sampled-data control systems using an improved exponential two-sided looped-functional approach

Stabilization of T–S fuzzy membership-function dependent H$$_\infty $$-based sampled-data control systems using an improved exponential two-sided looped-functional approach

A Sampled-Data-Based Secure Control Approach for Networked Control Systems Under Random DoS Attacks.

This article aims to analyze H∞ stability of a class of networked control systems (NCSs) under random denial of service (DoS) attacks and design a sampled-data-based state feedback security controller to mitigate the influence of attacks. Different from the existing random attacks, the information about the maximum duration time of DoS attacks can be captured by introducing a predesigned logical processor. Then, based on the periodic sampling technique, the probability of attack occurrence and the resultant number of maximum allowable consecutive packet dropouts can be calculated, which is quite significant to investigating the security problem of NCSs. A DoS-dependent security controller which makes full use of the attack probability information and the number of attack-induced packet dropouts is designed. A novel networked sampled-data system model is first established that enables us to deal with the random DoS attacks phenomena and the time-varying delay induced by attacks under a uniform framework. By structuring a suitable Lyapunov-Krasovskii functional, the relationship between mean square asymptotic stability and attack characteristics is obtained. Finally, the reliability and applicability of the presented control strategy in eliminating the influence of DoS attacks are validated by two practical engineering applications.

Controllability of Multilayer Networked Sampled-Data Systems.

The controllability analysis of networked systems is challenging due to their high dimensionality and complex structure. The influence of sampling on network controllability is rarely studied, making it an important topic to explore. In this article, the state controllability of multilayer networked sampled-data systems is studied, considering the deep network structure, multidimensional node dynamics, various inner couplings, and sampling patterns. Necessary and/or sufficient controllability conditions are proposed and validated by numerical and practical examples, requiring less computation than the classic Kalman criterion. Single-rate and multirate sampling patterns are analyzed, showing that adjusting the sampling rate of local channels can affect the controllability of the overall system. It is shown that the pathological sampling of single-node systems can be eliminated by an appropriate design of interlayer structures and inner couplings. In the case of systems with drive-response mode, the overall system may not lose controllability even when the response layer is uncontrollable. The results demonstrate that mutually coupled factors collectively affect the controllability of the multilayer networked sampled-data system.

The Small Gain Theorem in the Context of Sampled-Data Systems

The Small Gain Theorem in the Context of Sampled-Data Systems

Receding horizon estimation for multi‐rate sampled data systems under component‐based event‐triggered mechanisms: Handling delayed and degraded measurements

AbstractThe purpose of this article is to develop the receding horizon (RH) estimation for multi‐rate sampled systems with measurement delays and packet losses in the measurements. An event‐triggered transmission scheme is introduced to remove measurements that are unnecessary for the design of the estimator. The stochastic diagonal matrixes are introduced to represent the phenomenon of packet losses, where each component is subject to an individual Bernoulli process. The original system is firstly transformed into a delay‐free one by using the reorganized observation method. Further, a batch form and an iterative form of RH estimation are proposed by minimizing a given cost function that includes some terminal weighting terms based on the new system. The stability of the proposed RH estimation is guaranteed by the natural assumptions and a simulation instance is given to verify the effectiveness of the proposed method.

Analysis of sampled-data hybrid integrator-gain systems: A discrete-time approach

Hybrid integrator-gain systems (HIGS) are hybrid control elements used to overcome fundamental performance limitations of linear time-invariant feedback control, and have enjoyed recent successes in engineering applications such as high-precision motion systems. However, despite the relevance of digital implementations, the creation of sampled-data versions of HIGS and their formal analysis have not been addressed in the literature so far, and will form the topic of the present paper. Thereto, we present discrete-time HIGS elements, which preserve the main philosophy behind the operation of HIGS in continuous time. Moreover, stability criteria are presented that can be used to certify input-to-state stability of discrete-time and sampled-data HIGS-controlled systems based on both (i) (measured) frequency response data, and (ii) linear matrix inequalities (LMIs). A comparison between these stability criteria is presented as well. A numerical case study is provided to illustrate the application of the main results.

Asynchronous filtering for discrete-time T–S fuzzy sampled-data systems with improved quantization

This study delves into the asynchronous filtering problem within discrete-time Takagi–Sugeno (T–S) fuzzy sampled-data systems featuring non-periodic sampled measurements. A non-homogeneous Markov chain is utilized to capture the stochastic nature of the sampling period. The transition probability matrix of this non-homogeneous Markov process is time-varying and characterized using a multi-mode structure. To mitigate conservatism, a quantizer associated with the modes is implemented, where the quantization density is defined as the observed modes. Unlike existing approaches, there exists a discrepancy between the quantizer mode and the sampling mode, following a hidden Markov chain process. Additionally, a novel fuzzy asynchronous filter is introduced based on the observed modes to ensure the stochastic stability of the fuzzy system. Ultimately, the effectiveness of the proposed filter strategy is validated via a tunnel diode circuit model.

Observer-based fault-tolerant control design for a class of sampled-data nonlinear systems with bounded disturbances

Observer-based fault-tolerant control design for a class of sampled-data nonlinear systems with bounded disturbances

[formula omitted] sampled-data load frequency control with time-varying delays considering delay compensation

Time delays in load frequency control (LFC) systems may deteriorate the control performance or cause instability. How to mitigate such adverse effects of delays in a simple but effective way is worth investigating and motivates this work. For sampled-data LFC systems with time-varying delays, this paper introduces two delay compensation techniques, namely linear and division-based methods, aimed at enhancing the robustness of LFC. A stability criterion based on H∞ is derived to ensure LFC system stability under delay compensation. Building upon this criterion, we propose an H∞ controller optimization method to tune delay compensation controller gains offline by searching for a minimum H∞ disturbance attenuation level and effectively segmenting the geometric region formed by the delays. The effectiveness of the proposed delay compensation techniques and the controller design method is verified via numerical examples on an LFC system with both generation unit and energy storage participation.

An enhanced looped-functional framework for stability analysis of sampled-data systems

This paper enhances the looped-functional framework for sampled-data systems by using continuous Lyapunov functionals instead of xT(t)Px(t). The continuous Lyapunov functionals exploit the maximum allowable sampling interval compared with the traditional Lyapunov function xT(t)Px(t) in the conventional looped-functional framework. The enhanced looped-functional framework ensures the negativeness of the continuous Lyapunov functionals concerning the sampling instants and guarantees the stability of the sampled-data systems. Based on these continuous Lyapunov functionals, this paper constructs novel Lyapunov functionals with the looped-functional which not only exploits all available vectors related to sampling intervals but also introduces an additional interval which is zero at t=tk+1. Also, this paper proposes the stability criteria based on the enhanced looped-functional framework for the sampled-data systems with the asynchronous and synchronous samplings, respectively. The numerical examples show the effectiveness of the proposed framework.

Sliding-Mode Control for Sampled-Data Systems Over Fading Channels: Dealing With Randomly Switching Sampling Periods

Sliding-Mode Control for Sampled-Data Systems Over Fading Channels: Dealing With Randomly Switching Sampling Periods

Sampled-data controller synthesis using dissipative linear periodic jump-flow systems with design applications

In this paper, we will propose linear-matrix-inequality-based techniques for the design of sampled-data controllers that render the closed-loop system dissipative with respect to quadratic supply functions, which includes passivity and an upper-bound on the system’s H∞-norm as a special case. To arrive at these results, we model the sampled-data control system as a linear periodic jump-flow system, study dissipativity in terms of differential linear matrix inequalities (DLMIs) and then convert these DLMIs into a single linear matrix inequality. We will present three applications of these synthesis techniques: (1) passivity-based controller synthesis, as found in teleoperations, (2) input–output-response matching of a continuous-time filter with a discrete-time filter (by minimizing the H∞-norm of a generalized plant) and (3) a sampled-data controller redesign problem, where the objective is to find the best sampled-data controller, in the H∞-norm sense, for a given continuous-time controller. We will show that synthesizing sampled-data controllers leads to better closed-loop system behaviour than using a Tustin discretization of a continuous-time controller.

Stability analysis and control synthesis of hybrid time-varying linear systems using a discretization-based approach

A strategy for stability analysis and control design concerning a class of hybrid linear time-varying (LTV) systems is proposed in this paper. First, the transition matrix of the system is computed and then used to formulate the stability analysis condition, unifying both the flows and jumps into a single continuous-time framework and resulting in a straightforward methodology for hybrid dynamics. Such condition is then adapted to yield the proposed synthesis techniques, capable of generating a time-varying state-feedback gain to stabilize the hybrid LTV system. A discretization procedure is then proposed for both analysis and synthesis conditions, resulting on a numerically suitable approach that allows the adaptation of any LTV discrete-time synthesis technique to deal with the considered hybrid LTV systems. Finally, to highlight the possibilities of the methodology, the conditions are adapted for the stabilization of sampled-data time-varying systems. Numerical examples illustrate the validity and potentialities of the proposed techniques.

Improved stability and stabilization criteria for multi-rate sampled-data control systems via novel delay-dependent states

This paper aims to obtain less conservative stability and stabilization conditions for sampled-data linear systems with multiple sampling rates. To this end, three novel delay-dependent states resulting from sampling are introduced in the augmented state, enabling the exploitation of the sawtooth-type characteristics of the sampling-induced delay in both stability and stabilization processes. Additionally, a novel discontinuous function is included in Lyapunov–Krasovskii-based functional to enhance the capacity to extract more information from specific sampling pattern for each state. Especially, to strengthen the interdependence among the components of the augmented state, supplementary zero equalities are incorporated into the stability analysis conditions. Furthermore, by including a novel weighted state derivative in the augmented state, this paper proposes an effective method that can transform the parameter-dependent stability conditions into stabilization conditions formulated in terms of linear matrix inequalities. Finally, the validity and practicality of the proposed method are demonstrated through two illustrative examples.