Continuous-time Singular Systems Research Articles

Reliable induced [formula omitted] control for polytopic uncertain continuous-time singular systems with dynamic quantization

This paper considers the problem of state feedback control for a class of polytopic uncertain continuous-time singular systems with input quantization and actuator faults. The aim of this paper is to design the reliable controller and dynamic quantizer that ensure the considered closed-loop system is asymptotically stable and satisfies the prescribed induced L∞ performance constraint. The introduced proportional plus derivative state feedback controller can eliminate the structural restrictions of the system matrices, thus a more general sufficient condition is obtained for the problem. Finally, the four-mesh circuit is provided to demonstrate the effectiveness of the proposed induced L∞ control approach.

Fault detection filtering for continuous-time singular systems under a dynamic event-triggered mechanism

<p style='text-indent:20px;'>This paper focuses on the problem of fault detection filtering (FDF) for continuous-time singular systems via a dynamic event-triggered mechanism. Firstly, in order to reduce signal transmission and save network resources, a dynamic event-triggered mechanism is adopted. Compared with the static mechanism, the proposed method is more effective on reducing network transmission pressure since a dynamic variable is introduced. Secondly, a novel criterion is derived to guarantee the admissibility of the residual system with a certain <inline-formula><tex-math id="M1">\begin{document}$ \mathcal{H}_\infty $\end{document}</tex-math></inline-formula> performance. According to the derived conditions, a new method is given to codesign the desired filter and the event-triggered parameters. Finally, an example is employed to illustrate the validity of the proposed approach.</p>

Optimal control and zero-sum differential game for Hurwicz model considering singular systems with multifactor and uncertainty

Uncertainty theory is a new branch of mathematics concerned with the analysis of subjective indeterminacy. Based on the concept of uncertain theory, this paper considers optimal control and zero-sum differential game for multi-factor uncertain continuous-time singular systems with Hurwicz criterion, where dynamic systems are modelled by a type of uncertain differential equation driven by canonical Liu process. Using the approach of dynamic programming, the principle of optimality is proposed and then the equation of optimality is derived to resolve an uncertain control model. A two-player zero-sum uncertain differential game is further investigated based on the optimality equation above, and an equilibrium equation is presented to locate a saddle-point in the game. Finally, an example is discussed to illuminate the effectiveness of the results.

Fuzzy Energy-to-Peak Filtering for Continuous-Time Nonlinear Singular System

This article studies the energy-to-peak filter design problem for the continuous-time nonlinear singular system. A Takagi–Sugeno fuzzy model is constructed to represent the nonlinear plant. The article focuses on the fuzzy filter design for singular system, such that the formulated filtering error system is admissible (regular, impulse-free, and stable) and ensures the corresponding filtering performance in the singular system. By introducing a novel Lyapunov function, design conditions of the fuzzy filter for the continuous-time singular system are proposed in the light of linear matrix inequalities representations. Finally, a practical example and the relevant simulation results are provided to demonstrate the effectiveness and feasibility of the proposed energy-to-peak filter design approach.

Input-output Finite-time Stability of Switched Singular Continuous-time Systems

This paper is concerned with the problem of input-output finite-time stability (IO-FTS) for a class of switched singular continuous-time systems. First, the concept of IO-FTS is extended to switched singular systems. Then, by using the average dwell time switching approach and constructing multiple Lyapunov functions, a sufficient condition of IO-FTS for the considered system is presented in the form of linear matrix inequalities (LMIs). Furthermore, based on the derived conditions, a suitable state feedback controller is designed to stabilize the switched singular systems. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed technique.

Improved results on reachable set estimation of singular systems

Abstract This paper investigates the problem of reachable set estimation for a general class of continuous-time singular linear systems with time-varying delay. By employing a new Lyapunov functional candidate, a criterion with the help of linear matrix inequalities (LMIs) is developed utilizing the new inequality scaling method, free-weighting matrix and the time-delay segmentation method. The reachable set of the underlying system is bounded by the intersection of ellipsoids. The effectiveness of our results are demonstrated by the examples.

A Modified Functional Observer-Based EID Estimator for Unknown Continuous-Time Singular Systems

This paper presents the design of a linear quadratic analog tracker (LQAT) based on the observer–Kalman-filter identification (OKID) method and the design of a modified functional observer-based equivalent input disturbance (EID) estimator for unknown square–non-square singular analog systems with unknown input and output disturbances. First, an equivalent mathematical model of the singular analog system is presented to simulate the time response of continuous-time linear singular analog systems to arbitrary inputs via the model conversion method. Then, for the unknown singular analog system, it constructs a linear quadratic analog tracker with state feedback and feed-forward gains based on the off-line OKID method. Furthermore, it extends the design methodology of the EID estimator for strictly proper regular systems with unknown matched–mismatched input and output disturbances to proper regular systems. It is important to mention that the newly developed modified functional observer for proper systems is used to estimate the unknown EID of singular analog systems and that the constraints on the dimensions of unknown disturbances can be eliminated by using the newly proposed EID estimation method. The contributions of this paper can be listed as follows: (1) based on both the OKID method and the discrete-to-continuous model conversion, the simulation of the time responses of the continuous-time linear singular models (which are not feasible using existing MATLAB toolboxes) become feasible; (2) for effective control of the unknown singular analog system, an off-line OKID method is proposed to design an LQAT with state feedback and feed-forward gains; and (3) based on the newly developed modified functional observer for the reduced-order proper regular system, the original EID estimator in the literature is newly extended to estimate the EID from the unknown strictly proper singular analog system, without the original dimensional constraints of the disturbances. It is important to mention that the disturbances of interest can be unknown matched–mismatched input and output disturbances.

Event-Triggered H-Infinity Control for Continuous-Time Singular Networked Cascade Control Systems With State Delay

This paper is concerned with the problems of modeling, stabilization, and H control for continuous-time singular networked cascade control systems (SNCCSs) with state delay and event-triggered control. An event-triggered scheme is firstly introduced to this system for utilizing the network bandwidth resources efficiently. Considering the effects of both time-varying network-induced delay and event-triggered control, a singular networked cascade control system (SNCCS) model is established. By constructing a suitable Lyapunov-Krasovskii functional, sufficient condition of admissibility for this system is proposed, and the co-design method of event-triggered parameter, primary state feedback controller and secondary state feedback controller are also derived. Furthermore, H ∞ control is concerned for SNCCS via linear matrix inequality (LMI) technique. Finally, a simulation example considering a heating furnace with the structure of SNCCS and event-triggered control is given to illustrate the effectiveness of the proposed method, where it can be seen this method is superior to the existing one with periodic control.

A positive real lemma for singular hybrid systems

Abstract This paper introduces a positive real lemma for continuous-time singular hybrid systems. The necessary and sufficient condition of stochastic admissibility and strict passivity for the singular hybrid systems is obtained in terms of linear matrix inequalities. The sufficient condition is derived by using mode-dependent Lyapunov function. In this step, two slack variables are inserted to make the proposed condition be necessary and sufficient condition in terms of strict linear matrix inequalities. Then, to prove the necessary condition, the positive real lemma for the hybrid system is proposed. Since the admissible singular system can be reformulated into stable normal system, the positive real lemma for the hybrid system holds. Thus, we give a necessary condition by constructing the solution of the proposed lemma from that of the hybrid systems.

Finite-time decentralized H∞ control for singular large-scale systems

Abstract In this paper, the definition of finite-time robust H∞ control for linear continuous-time singular large-scale systems is presented. The main aim of this paper is to design a decentralized state feedback controller which ensures that the closed-loop system is finite-time bounded (FTB), and the effect of the disturbance input on the controller output, meanwhile, is reduced to a prescribed level. A sufficient condition is presented for the solvability of this problem, which can be reduced to a feasibility problem involving linear matrix inequalities (LMIs). A detailed solving method is proposed for the restricted linear matrix inequalities. Finally, examples are given to show the validity of the methodology.

On Positive Realness for Stochastic Hybrid Singular Systems

This paper deals with the problem of passivity analysis and passivity-based synthesis for continuous-time stochastic hybrid singular systems (SHSSs). First, a set of linear matrix inequalities for the stochastic admissibility and passivity, which is also known as the positive real lemma, is obtained for continuous-time SHSSs. The proposed condition successfully holds a necessary and sufficient condition for the positive realness of SHSSs, whereas the existing papers in the literature have been handled only sufficient conditions. Next, the passivity-based control synthesis problem is also considered based on the new positive real lemma. The passivity-based stabilization criterion for the closed-loop system with its mode-dependent state-feedback control is expressed in terms of matrix inequality. Thus, by introducing an additional slack matrix to the non-convex conditions, the feasible conditions for the control gain are obtained in terms of linear matrix inequalities. Finally, a numerical example is provided to show the effectiveness of the result.

Computational Method Based on Reflection Operator for Solving a Class of Fractional Optimal Control Problem

Abstract A computational method based on reflection operator and Grunwald-Letnikov (GL) formulation for solving fractional optimal control problem (FOCP) of continuous-time singular system (SS) is presented in this paper. Dynamics of the system is described by the differential equations of fractional order in the sense of either Caputo or Riemann-Liouville (RL) fractional derivatives (FDs). In this method, first we convert right FD into left FD by using reflection operator and then apply GL formulation for solving the FOCP. Two examples are illustrated to demonstrate the efficacy of the computational method.

Preview Tracking Control for Continuous-Time Singular Interconnected Systems

This paper proposes and investigates a problem of preview tracking control for a class of continuous-time singular interconnected systems. Firstly, the related items are deleted to obtain several isolated subsystems with low dimensions. An error system is constructed for each isolated subsystem so that the tracking error is included in the state vector of the error system; then, the tracking problem is transformed into a regulation problem. Secondly, the preview tracking controller is designed for each error system and obtained controllers are combined as the controller of the error system of the singular interconnected system. Thirdly, the Lyapunov function method is utilized to determine the constraints of the related terms so that the closed-loop system of the error system of the singular interconnected system is stable under the action of the controller obtained. Finally, the preview tracking controller of the singular interconnected system is obtained from the relationship between the error system and the original system. A numerical simulation algorithm for continuous-time singular systems is also proposed in this paper. The numerical simulation illustrates the effectiveness of the theoretical results.

Preview control for continuous-time singular stochastic systems

In this paper, the problem of preview control for continuous-time singular stochastic systems is studied by the augmented error system approach. First, a static output feedback is introduced to make the closed-loop system impulse-free. And through the second restricted equivalent transformation, the continuous-time singular stochastic system is transformed into a normal stochastic system and some algebra equations. Then, an assistant system is designed to overcome the difficulty of trying to make derivation to a stochastic system like in deterministic system condition. And the stochastic system after the transformation is translated to the assistant system. In order to make the output of the singular system track the reference signal as accurately as possible without static error, an integrator is introduced. Based on the system after the translation and the error equation, an augmented error system is constructed with the state vector, the error vector and the reference signal. Finally, the tracking problem for the singular stochastic system is transformed into the optimal regulating problem for the augmented error system. By the dynamic programming method, the optimal preview controller for the original singular stochastic system is obtained. The existence and uniqueness solution of the Riccati equation is discussed and the numerical analysis shows the effectiveness for the preview controller designed in this paper.

Finite-Time Stability and Stabilization of Fractional-Order Switched Singular Continuous-Time Systems

The finite-time stability and stabilization of a class of fractional-order switched singular continuous-time systems with order $$0<\alpha <1$$ are investigated in this paper. First, by employing the average dwell time switching technique, together with the introduction of multiple Lyapunov functions, some sufficient conditions of the finite-time stability and finite-time boundedness are derived for the considered system. Second, based on the obtained conditions, suitable state feedback controllers can be designed if a set of linear matrix inequalities are feasible. Finally, an illustrative example is presented to show the effectiveness of the proposed results.

Non-fragile consensus control for singular multi-agent systems with Lipschitz nonlinear dynamics

In this paper, the problem of non-fragile consensus control for continuous-time singular multi-agent systems with respect to Lipschitz nonlinear dynamics is investigated. Considerations are that the concerned nonlinear singular dynamical agents communicate in an undirected connected topology and the states of all agents achieve consensus by the designed protocol which is subject to norm-bounded parametric uncertainty. On the basis of nonsingular transformation, non-fragile consensus performance analysis for the concerned multi-agent systems is converted into asymptotical stabilization problems of some lower dimensional subsystems. By exploiting the structure of the nonsingular transformation matrix, moreover, the impacts of the Lipschitz nonlinear dynamics are eliminated. Benefitting from the introduced free-weighting matrices, sufficient conditions for non-fragile consensus controller design are formulated in terms of linear matrix inequalities. Furthermore, the explicit dynamical expression and the determined initial states of the consensus function are also given. Numerical examples are exploited to illustrate effectiveness of the derived results.

State bounding estimation for a linear continuous-time singular system with time-varying delay

This paper investigates the problem of a state bounding estimation for a linear continuous-time singular system with time-varying delay. By employing the maximal Lyapunov–Krasovskii functional and applying the new free-matrix-based integral inequality, some proper conditions are derived in terms of LMIs and a bounding estimation lemma and set are obtained for the studied singular system.

Finite-time guaranteed cost controller design for uncertain linear continuous-time singular systems

This article concerns the finite-time robust guaranteed cost control problem for a class of linear continuous-time singular systems with norm-bounded uncertainties. In this study, the problem is to design a state feedback controller such that the closed-loop system is finite-time stable, and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. By constructing an appropriate Lyapunov function, a sufficient condition for the finite-time robust stability of the system based on linear matrix inequality (LMI) is established. Furthermore, the sufficient condition for the existence of the guaranteed cost controller is formulated in terms of LMIs, which can make the closed-loop uncertain singular system finite-time robust stable. Finally, two numerical examples are given for illustration of the proposed theoretical results.

A Robust H∞ Filter for Uncertain Continuous-Time Affine Nonlinear Singular Systems

In the present paper, the problem of robust H∞ filtering for continuous-time affine nonlinear singular systems (ANSSs) with norm-bounded uncertainty is studied. Employing Luenberger-like and certainty equivalent structures, and based on the differential game theory, sufficient conditions for the existence of such filters are derived. These conditions are in the form of a generalized Hamilton–Jacobi–Isaacs (GHJI) inequality and the output injection gain of each filter is obtained as a function of the corresponding GHJI inequality solution. Numerical simulations are provided to demonstrate the applicability of the proposed approach. The results show that the adopted method not only perfectly achieves the estimation goals in the presence of model uncertainties but also outperforms some existing results for known (certain) systems.

Finite-time robust decentralized control for uncertain singular large-scale systems with exogenous disturbances

AbstractThis paper considers the problem of finite-time robust decentralized control for uncertain continuous-time singular large-scale systems with exogenous disturbances (UCSLSSED). The concept of finite-time robust decentralized stabilization for UCSLSSED is introduced by definition of finite-time stability for uncertain continuous-time large-scale systems with exogenous disturbances. The analyses of finite-time robust bounded and finite-time robust stabilization for UCSLSSED are done. The design approach of finite-time robust decentralized state feedback controller is also given. Finally, an illustrative example is provided to show the effectiveness of the proposed method.