Uncertain Singular Systems Research Articles

Fault-tolerant control against actuator failures for uncertain singular fractional order systems

<p style='text-indent:20px;'>A method of designing observer-based feedback controller against actuator failures for uncertain singular fractional order systems (SFOS) is presented in this paper. By establishing actuator fault model and state observer, an observer-based fault-tolerant state feedback controller is developed such that the closed-loop SFOS is admissible. The controller designed by the proposed method guarantees that the closed-loop system is regular, impulse-free and stable in the event of actuator failures. Finally, a numerical example is given to illustrate the effectiveness of the proposed design method.</p>

Robust Disturbance Rejection in Uncertain Singular Systems Using Equivalent-Input-Disturbance Method Based on Output Feedback Control

A robust disturbance-rejection problem for an uncertain singular system is considered in this paper. An equivalent-input-disturbance (EID) method is applied to improve disturbance-rejection performance. At first, the disturbance estimation is obtained by the EID method; Then, the disturbance estimation is compensation to the control input channel to offset the adverse effect of external disturbance and uncertainties on the system. Two sufficient and necessary conditions using linear matrix inequality are obtained, which can guarantee the admissibility (regularity, non-impulsiveness, and stability) for the closed-loop control system. In addition, output-feedback control laws (static, dynamic) and observer gain are obtained using the singular value decomposition method. A numerical example and simulation studies prove the validity and feasibility of the presented method.

Adaptive Robust H∞ Sliding Mode Control for Singular Systems with Time-varying Delay and Uncertain Derivative Matrix

This paper considers the problem of sliding mode control (SMC) design for a class of nonlinear singular systems with time-varying delay and uncertainties, especially with uncertainties in the derivative matrix. By taking uncertainties of the derivative matrix into account, the state augmentation transformation is constructed such that uncertainties of the derivative matrix are eliminated. Then an appropriate integral-type sliding surface function is designed. And the resulting sliding mode dynamics is an uncertain singular time-varying delay system. A delay-dependent sufficient condition which guarantees the sliding mode dynamics to be admissible with H∞ performance is established. A new version of stabilization solvability condition is then proposed in terms of linear matrix inequality (LMI), which determines the undetermined parameter K in both the sliding surface function and the SMC laws. Moreover, two distinctive controllers (i.e., a SMC law and an adaptive SMC law) are synthesized such that the finite-time reachability of the predesigned sliding surface can be ensured. Finally, simulation examples are given to demonstrate the effectiveness and the merits of the proposed theory.

Robust H∞ control of uncertain singular systems based on equivalent‐input‐disturbance approach

AbstractIn this paper, a robust H∞ control problem is considered for an uncertain singular system. An active disturbance rejection method called equivalent input disturbance (EID) is used to reduce the influence of exogenous disturbances and uncertainties on the system. At the first, there exists an EID, which can produces the same effect on the system as disturbances and uncertainties do in the control channel according to the EID concept. Then, an EID estimator is constructed to estimate the influence of EID on the system. Finally, based on Lyapunov stability theory, a static output feedback‐based robust H∞ controller combined with EID estimate is designed, guaranteeing that closed‐loop system is admissible (regular, impulse‐free, and stable) with a prescribed H∞ performance level. Compared with traditional H∞ control method, H∞ control based on EID method improve the control performance of the system. A numerical example demonstrates the validity of the method.

Robust admissibility and stabilization of uncertain singular fractional-order linear time-invariant systems

This paper addresses the robust admissibility problem in singular fractional-order continuous time systems. It is based on new admissibility conditions of singular fractional-order systems expressed in a set of strict linear matrix inequalities &#x0028 LMIs &#x0029. Then, a static output feedback controller is designed for the uncertain closed-loop system to be admissible. Numerical examples are given to illustrate the proposed methods.

Robust H∞ Control For Uncertain Singular Neutral Time-Delay Systems

The present paper attempts to investigate the problem of robust H ∞ control for a class of uncertain singular neutral time-delay systems. First, a linear matrix inequality (LMI) is proposed to give a generalized asymptotically stability condition and an H ∞ norm condition for singular neutral time-delay systems. Second, the LMI is utilized to solve the robust H ∞ problem for singular neutral time-delay systems, and a state feedback control law verifies the solution. Finally, four theorems are formulated in terms of a matrix equation and linear matrix inequalities.

Finite-time [formula omitted] sliding mode control for uncertain singular stochastic system with actuator faults and bounded transition probabilities

This paper investigates the finite-time H∞ control problem for singular Markovian jump system with actuator fault through the sliding mode control approach. Based on the observer, the augment system can be constructed with time-varying delays and actuator failure. Continuous actuator failure model is considered in this paper. Next, a sliding surface is considered under which sufficient conditions are given to make sure the augment system is singular stochastic H∞ finite-time bounded. And the sliding mode control law is synthesized to guarantee the reachability of the sliding surface in a short time interval. The state feedback controller gain matrices and observer gain matrices are obtained by solving the relevant linear matrix inequalities. Decoupling method has been adopted for the coupled variables. Finally, simulation examples illustrate the validity of the proposed method.

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.

Robust observer-based sliding mode control for nonlinear uncertain singular systems with time-varying delay and input non-linearity

This article focuses on the output-feedback sliding mode control design problem for a class of non-linear singular systems with time-varying delay and uncertainties. More precisely, we aim to design an adaptive observer-based sliding mode controller for such class of systems. The appealing aspects of this approach include (i) based on an appropriate Lyapunov–Krasovskii functional, a delay-dependent sufficient condition is established to guarantee the autonomous singular system to be admissible and (ii) by constructing an observer to estimate the system states, an integral sliding mode surface and an adaptive observer-based sliding mode controller are designed to ensure the closed-loop singular system to be insensitive to all admissible uncertainties and satisfies the reaching condition. The developed results are tested on three representative examples to illustrate the theoretical developments.

Robust Impulsive Stabilization of Uncertain Nonlinear Singular Systems with Application to Transportation Systems

We consider the robust asymptotical stabilization problem for uncertain singular systems. We design a new impulsive control technique to ensure that the controlled singular system is robustly asymptotically stable and hence derive the corresponding stability criteria. These sufficient conditions are expressed in the form of algebra matrix inequalities and can be implemented numerically. We finally provide a numerical example of a transportation system to illustrate the effectiveness and usefulness of the proposed criteria.

H∞ robust control based on event‐triggered sampling for hybrid systems with singular Markovian jump

The problem of H∞ robust control based on event‐triggered sampling for a class of singular hybrid systems with Markovian jump is considered in this paper. The primary object of this paper here is to design the event‐triggered sampling controller for a class of uncertain singular Markovian systems, and two fundamental issues on mean square exponential admissibility and H∞ robust performance are fully addressed. By making use of a suitable Lyapunov functional, in combination with both infinitesimal operator and linear matrices inequalities(LMIs), the sufficient criteria are derived to guarantee the controlled singular hybrid system with Markovian jump is robustly exponentially mean‐square admissible and has a prescribed H∞ performance γ. Finally, a typical RLC circuit system is given to show the effectiveness of the proposed control method.

A delay-range-dependent stabilization of uncertain singular time-delay systems with one-sided Lipschitz nonlinearities subject to input saturation

This paper investigates the problem of delay-range-dependent robust stabilization for nonlinear singular systems with time-delay subject to some constraints. In practice, the control problem of dynamic systems faces a variety of constraints such as: presence of input saturation; one-sided Lipschitz nonlinearities; model uncertainties; and time-varying delay. The interaction of both algebraic and differential equations in singular systems with delayed state variables adds some complexities and difficulties in the procedure of analysis and design of singular time-delay systems. Moreover, the one-sided Lipschitz nonlinearity condition, which is less conservative than the well-known Lipschitz condition, is considered while the presence of actuator saturation also imposes additional complexity in the procedure of controller design. In this regard, by choosing an appropriate Lyapunov–Krasovskii functional with applying the free-weighting matrices approach, the sufficient conditions are derived as linear matrix inequalities which guarantee the asymptotic stability of the resulting uncertain closed-loop singular system. Finally, computer simulations are provided to verify the theoretical results.

Robust sideslip angle observer with regional stability constraint for an uncertain singular intelligent vehicle system

The sideslip angle is an important state parameter for vehicle stability control; in this study, a robust sideslip angle observer with regional stability constraint is presented. In order to achieve more accurate sideslip angle estimation, the vehicle heading angle and yaw angle are distinguished and the relational expression between vehicle heading angle, yaw angle and sideslip angle was applied to the singular vehicle modelling process. Considering the time-varying tire cornering stiffness, the uncertain singular vehicle model is established by integrating the singular vehicle dynamic equation and model uncertainty. Then, a robust sideslip angle observer whose pole assignment has the regional stability constraint is designed. Simulation studies and experimental results illustrate the effectiveness of the proposed sideslip angle estimation method.

Robust Observer-based Control Design for Singular Systems with Delays in States

In this paper, the robust observer-based control problem for uncertain singular time delay systems is investigated. The approach is based on using Finsler's lemma. First, delay-dependent linear matrix inequality (LMI) conditions are obtained which, guarantee that the nominal unforced system is regular, impulse free, and stable. Then, with the help of obtained admissibility criterion, an observer-based controller is given by solving a set of LMIs. Finally, some simulations are provided to demonstrate the effectiveness of the obtained results.

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.

The stability analysis and control of uncertain singular biological economic system with invasion of alien species based on sliding mode control

The stability analysis and control of uncertain singular biological economic system with invasion of alien species based on sliding mode control

Delay-dependent robust resilient $$H_\infty $$ H ∞ control for uncertain singular time-delay system with Markovian jumping parameters

This paper is concerned with the delay-dependent robust resilient $$H_\infty $$ control problem for uncertain singular time-delay system with Markovian jumping parameters. First, a delay-dependent bounded real lemma in terms of linear matrix inequalities is established, which guarantees the nominal Markovian jump singular system to be regular, impulse free and stochastically stable. Then, based on this condition, sufficient conditions in terms of LMIs are given to ensure the existence of the desired robust resilient $$H_\infty $$ controllers. The uncertainties of the controllers are considered in two cases, that is the additive controller gain uncertainties and the multiplicative controller gain uncertainties. Finally, numerical examples illustrate the applicability of the results proposed in this paper.

Finite-Time Robust H∞ Control for Uncertain Linear Continuous-Time Singular Systems with Exogenous Disturbances

Singular systems arise in a great deal of domains of engineering and can be used to solve problems which are more difficult and more extensive than regular systems to solve. Therefore, in this paper, the definition of finite-time robust H∞ control for uncertain linear continuous-time singular systems is presented. The problem we address is to design a robust state feedback controller which can deal with the singular system with time-varying norm-bounded exogenous disturbance, such that the singular system is finite-time robust bounded (FTRB) with disturbance attenuation γ. Sufficient conditions for the existence of solutions to this problem are obtained in terms of linear matrix equalities (LMIs). When these LMIs are feasible, the desired robust controller is given. A detailed solving method is proposed for the restricted linear matrix inequalities. Finally, examples are given to show the validity of the methodology.

New insight into reachable set estimation for uncertain singular time-delay systems

This paper investigates the problem of reachable set estimation for a class of uncertain singular systems with time-varying delays from a new point of view. Our consideration is centered on the design of a proportional-derivative state feedback controller (PDSFC) such that the considered singular system is robustly normalizable and all the states of the closed-loop system can be contained by a bounded set under zero initial conditions. First, a nominal singular time-delay system is considered and sufficient conditions are obtained in terms of matrix inequalities for the existence of a PDSFC and an ellipsoid. In this case, the considered system is guaranteed to be normalizable and the reachable set of the closed-loop systems is contained by the ellipsoid. Then, the result is extended to the case of singular time-delay systems with polytopic uncertainties and relaxed conditions are derived by introducing some weighting matrix variables. Furthermore, based on the obtained results, the reachable set of the considered closed-loop singular system can be contained in a prescribed ellipsoid. Finally, the effectiveness of our results are demonstrated by two numerical examples.

Passification of Uncertain Singular Semi-Markovian Jump Systems With Actuator Failures Via Sliding Mode Approach

This paper investigates the problem of robust passivity-based sliding mode control (SMC) for uncertain singular systems with semi-Markov switching and actuator failures. The attention is focused on designing a common sliding surface to weaken the jumping effect and developing a sliding mode controller to accommodate to actuator faults for passification of the singular semi-Markovian jump system. Based on linear matrix inequality technique, sufficient conditions are derived to ensure the closed-loop system to be stochastically admissible and robustly passive. Then the finite-time reachability of the sliding surface is guaranteed by the proposed SMC law. Finally, a numerical example is provided to demonstrate the effectiveness of the obtained result.