Design Of Linear Systems Research Articles

Output formation-containment analysis and design for general linear time-invariant multi-agent systems

Output formation-containment control problems for general linear time-invariant multi-agent systems with directed topologies are dealt with. Output formation-containment means that the outputs of leaders achieve the predefined formation, and at the same time the outputs of followers converge to the convex hull formed by the outputs of leaders. Firstly, static output protocols are presented for leaders and followers respectively. Then output formation-containment problems of multi-agent systems are transformed into asymptotic stability problems. Sufficient conditions with less computation complexity are proposed for multi-agent systems to achieve the output formation-containment. An explicit expression for the time-varying output formation reference function is derived to describe the macroscopic movement of the whole output formation-containment. Explicit expressions to describe the relationship among the outputs of followers, the time-varying output formation for the leaders and the output formation reference are derived. It is proven that the outputs of followers not only converge to the convex hull formed by those of leaders but also achieve certain time-varying formation specified by the convex combination of the desired output formation for the leaders. Moreover, an approach to determine the gain matrices in the protocols is given for multi-agent systems to achieve the output formation-containment. Finally, numerical simulations are provided to demonstrate the effectiveness of the theoretical results.

New unified [formula omitted] dynamic observer design for linear systems with unknown inputs

In this paper, a unified H∞ dynamic observer (UO) is proposed for a class of linear systems in the presence of unknown inputs and disturbances. It generalizes the existing results on the proportional observer (PO), the proportional integral observer (PIO) and the dynamic observer (DO). The design approach of the UO is derived from the solution of the linear matrix inequality (LMI), based on the new dynamic observer formulation and the solution of the algebraic constraints obtained from the unbiased estimation error. A numerical example is provided to show the applicability and the performance of our results.

Robust switched controller design for linear continuous-time systems

Abstract In this paper we study a novel approach to the design of a robust switched controller for continuous-time systems described by a novel robust plant model using quadratic stability and multi parameter dependent quadratic stability approaches. In the proposed design procedure with an output feedback a novel quadratic cost function is proposed which allows to obtain different performance dependence on the working points. Finally a numerical examples are investigated.

A determinant criterion for stability analysis and design of linear discrete systems

A determinant criterion for stability analysis and design of linear discrete systems

Low-Order Stabilizer Design for Discrete Linear Time-Varying Internal Model-Based System

This paper focuses on the low-order stabilizer design for linear time-varying (LTV) internal model-based system in the discrete time domain. While an output feedback gain injection-based stabilizer was proposed for continuous LTV systems in previous work, the synthesis in discrete domain has its unique challenges, and the approach formulated in the continuous domain cannot be directly applied. In this paper, the stabilization for LTV internal model-based control in the discrete setting is formulated, its challenges are revealed, and two control synthesis methods are presented. The merits and limitations of both approaches are discussed and then further studied through simulation and experimental investigations.

Sliding mode control design for linear systems subject to quantization parameter mismatch

This paper is concerned with the sliding mode control design for linear systems considering the mismatch between quantization sensitivity parameters generated at the coder and decoder sides. By analyzing the working principle of the encoder/decoder, and the feature of the digital communication channel, a mismatched relation between the quantization parameters is formed by using a time varying ratio model which includes the existing results as special cases. Sequently, based on the established mathematical model, sliding mode control laws are designed to ensure the asymptotical stability of the whole dynamical system. Finally, examples are shown to verify the validity of the theoretical results.

Iterative learning control design for linear discrete-time systems with multiple high-order internal models

This work is focused on the iterative learning control (ILC) design for linear discrete-time systems with iteration-varying factors, including reference, initial state, and exogenous disturbances. First, multiple high-order internal models (HOIMs) are given for various iteration-varying factors. The reference is generated by an HOIM, and the initial state and the exogenous disturbances ultimately satisfy HOIMs but do not strictly follow HOIMs in finite iteration interval. Then, a new ILC scheme, a special high-order ILC (HO-ILC), is constructed according to an augmented HOIM that is the aggregation of all HOIMs. For simplicity, the case with only iteration-varying reference is first considered, where the asymptotic stability and monotone convergence based ILC design methods are both presented by using the 2-D analysis approach. Next, more iteration-varying factors are further considered. In this situation, the HOIM-based ILC is transformed into a controller design problem of a 2-D Roesser model with non-zero boundary states and disturbances, where the 2-D H∞ performance is studied. In consequence, an ILC design criterion is presented to achieve perfect tracking and 2-D H∞ performance. For comparison, the monotone convergence based ILC design method is extended to the situation with more iteration-varying factors. Utilizing information provided by the multiple HOIMs, it is verified that HO-ILC outperforms low-order ILC (LO-ILC) in presence of iteration-varying factors. Meanwhile, the 2-D H∞ based ILC is shown to be superior to the monotone convergence based ILC. Finally, a microscale robotic deposition system with iteration-varying factors is given to illustrate the advantage of the proposed 2-D H∞ based ILC.

On fault detection filters design with unitary transfer function matrices

An adaptation of unitary system principle in fault detection filter design for continuous-time linear MIMO systems is presented in the paper. The conformation is based on an enhanced fault residual transfer function matrix with unitary construction and offers the key advantages on providing high residual sensitivity with respect to faults. Reflecting the emplacement of singular values in unitary construction, an associated structure of linear matrix inequalities with built-in structured constraints is outlined to verify the filter stability. The proposed design conditions are verified by the numerical illustrative example.

LQR-Based Optimal Distributed Cooperative Design for Linear Discrete-Time Multiagent Systems.

In this paper, a novel linear quadratic regulator (LQR)-based optimal distributed cooperative design method is developed for synchronization control of general linear discrete-time multiagent systems on a fixed, directed graph. Sufficient conditions are derived for synchronization, which restrict the graph eigenvalues into a bounded circular region in the complex plane. The synchronizing speed issue is also considered, and it turns out that the synchronizing region reduces as the synchronizing speed becomes faster. To obtain more desirable synchronizing capacity, the weighting matrices are selected by sufficiently utilizing the guaranteed gain margin of the optimal regulators. Based on the developed LQR-based cooperative design framework, an approximate dynamic programming technique is successfully introduced to overcome the (partially or completely) model-free cooperative design for linear multiagent systems. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design methods.

Consensus analysis and design of linear interconnected multi-agent systems

We deal with the state consensus problem of a general Linear Interconnected Multi-Agent System (LIMAS) under a time-invariant and directed communication topology. Firstly, we propose a linear consensus protocol in a general form, which consists of state feedback of the agent itself and feedback form of the relative states between the agent and its neighbors. Secondly, a state-linear-transformation is applied to equivalently transform the state consensus problem into a partial stability problem. Based on the partial stability theory, we derive a sufficient and necessary criterion of consensus convergence, which is expressed via the Hurwitz stability of a real matrix constructed from the parameters of the agent models and the protocols, and present an analytical formula of the consensus function. Lastly, we propose a design procedure of the gain matrices in the protocol by solving a bilinear matrix inequality.

Function observer based event-triggered control for linear systems with guaranteed L-gain

This paper is devoted to event-triggered control design for linear systems based on function observer. More specifically, the main purpose is to design event-triggered mechanisms that trigger transmissions when the difference between the current value of the system and its previously transmitted value which includes the plant output or the function observer output exceeds an additional threshold. For such an eventtriggered mechanism, we derive conditions in terms of matrix inequality to guarantee the stability as well as longer inter-event time. We propose two approaches to investigate the closed-loop model, namely, reformulating the event-triggered control system as a hybrid system and interpreting the event-induced error as exogenous disturbance. Furthermore, the minimum inter-event time is guaranteed to be strictly positive. An example is presented to illustrate the feasibility and efficiency of the theoretic results.

Analysis, design, and estimation of linear equality-constrained dynamic systems

The state of many dynamic systems evolves subject to some equality constraints. Most existing work focuses on developing state estimation algorithms for an equality-constrained dynamic system assuming the system is given. How to design and analyze such a system is rarely addressed, even though it is critically important for application and performance evaluation. In this paper, we first analyze the underlying structural information of linear equality-constrained (LEC) dynamic systems through direct elimination. It is found that the process noise of such a system is state dependent in general. This means that existing formulations of such a system are quite limited. Based on the analysis, we then propose a new systematic way to design LEC systems. The key idea is to design only the unconstrained part of the system. Unlike existing system conversion-based design techniques, in our work the desired model class is given and only the distributions of the initial state and process noise need to be determined, which is comparatively easier. To handle state dependency of the process noise, a new constrained state estimation algorithm based on direct elimination is also proposed. Three examples are provided to illustrate the effectiveness of the proposed methods of analysis, design, and estimation, respectively.

Containment analysis and design for general linear multi-agent systems with time-varying delays

Containment analysis and design problems for general high-order linear time-invariant multi-agent systems with time-varying delays are studied, where the interaction topology is directed. Using the state information of each agent and neighboring agents, a protocol with time-varying delays is constructed, where the motion modes of the leaders can be specified. Based on Lyapunov–Krasovskii stability theory, sufficient conditions for general linear multi-agent systems with time-varying delays to achieve containment are proposed which only include four linear matrix inequalities independent of the number of agents. Moreover, an approach to determine the gain matrices in the protocol is presented. Finally, a numerical example is given to demonstrate the effectiveness of the obtained theoretical results.

State-feedback control for LPV systems with interval uncertain parameters

This paper proposes a state-feedback controller design for linear parameter-varying systems with interval uncertain parameters that are interval-type uncertain weight functions for convex combinations of linear subsystems. The proposed controller hires secondary convex parameters generated through the lower and upper boundaries of the interval uncertain parameters. The resulting stabilization condition is expressed in terms of parameterized linear matrix inequalities, which are then converted into linear matrix inequalities using a parameter relaxation technique. The simulation results illustrate the robustness of the proposed controller.

Synthesizing Configurable Biochemical Implementation of Linear Systems from Their Transfer Function Specifications.

The ability to engineer synthetic systems in the biochemical context is constantly being improved and has a profound societal impact. Linear system design is one of the most pervasive methods applied in control tasks, and its biochemical realization has been proposed by Oishi and Klavins and advanced further in recent years. However, several technical issues remain unsolved. Specifically, the design process is not fully automated from specification at the transfer function level, systems once designed often lack dynamic adaptivity to environmental changes, matching rate constants of reactions is not always possible, and implementation may be approximative and greatly deviate from the specifications. Building upon the work of Oishi and Klavins, this paper overcomes these issues by introducing a design flow that transforms a transfer-function specification of a linear system into a set of chemical reactions, whose input-output response precisely conforms to the specification. This system is implementable using the DNA strand displacement technique. The underlying configurability is embedded into primitive components and template modules, and thus the entire system is adaptive. Simulation of DNA strand displacement implementation confirmed the feasibility and superiority of the proposed synthesis flow.

Simplified derivations of time-weighted quadratic functionals used in optimal control and filtering applications

In this article, we present simple alternative derivations for efficient evaluation of a matrix integral that has applications in optimal control and filtering, stability, controllability, observability, and controller design of linear time-invariant systems. The quadratic matrix integral (functional) is computed in terms of solutions of a sequence of algebraic Lyapunov equations. We present also a method to efficiently solve the obtained sequence of algebraic Lyapunov equations.

Unknown input observer for linear time-delay systems

This paper investigates an unknown input observer design for a large class of linear systems with unknown inputs and commensurate delays. A Luenberger-like observer is proposed by involving only the past and actual values of the system output. The required conditions for the proposed observer are considerably relaxed in the sense that they coincide with the necessary and sufficient conditions for the unknown input observer design of linear systems without delays.

A new view of anti-windup design for uncertain linear systems in the frequency domain

This paper presents a new perspective on the stability problem for uncertain LTI feedback systems with actuator input amplitude saturation. The solution is obtained using the quantitative feedback theory and a 3 DoF non-interfering control structure. Describing function (DF) analysis is used as a criterion for closed loop stability and limit cycle avoidance, but the circle or Popov criteria could also be employed. The novelty is the combination of a controller parameterization from the literature and describing function-based limit cycle avoidance with margins for uncertain plants. Two examples are given. The first is a benchmark problem and a comparison is made with other proposed solutions. The second is an example that was implemented and tested on an X-Y linear stage used for nano-positioning applications. Design and implementation considerations are given. An example is given on how the method can be extended to amplitude and rate saturation with the help of the generalized describing function, and a novel anti-windup compensation structure inspired by previous contributions. Copyright © 2015 John Wiley & Sons, Ltd.

Two-Stage Feedback Control Design for a Class of Linear Discrete-Time Systems With Slow and Fast Modes

In this paper, we first review the new algorithm for the two-stage feedback controller design of linear discrete-time systems, and then provide conditions for its applicability. The design algorithm is specialized and simplified for a class of linear systems with slow and fast modes (multitime scale systems or singularly perturbed systems). The proposed design significantly reduces computational full-state feedback design requirements and provides independent and accurate feedback controller design techniques in slow and fast time scales. We present also conditions needed for applicability of the proposed two-stage design in two time scales. The power of the two-stage design lies in the fact that different types of controllers can be designed for different subsystems using the corresponding feedback gains obtained by performing calculations only with the subsystem (reduced-order) matrices.

H∞ dynamical observers design for linear descriptor systems. Application to state and unknown input estimation

The present paper considers the H∞ observers design problem for descriptor systems. The goal is to design a dynamical observer such that the resulting dynamic estimation error is stable while the transfer function from the disturbance input to this error satisfies a prescribed H∞ norm level. Conditions for the solvability of this problem are obtained in terms of a set of linear matrix inequalities (LMIs). An extension to a simultaneous estimation of state and unknown input for descriptor systems is presented. A numerical example is provided to illustrate our approach.