Controller Gain Matrices Research Articles

New alternative convex conditions on exponential stability and stabilisation of switched positive linear systems with dwell time

This study is concerned with dwell time stability and stabilisation problems of switched positive linear systems (SPLSs). The dwell time refers to minimum dwell time and constant dwell time. Several stability conditions for primal and transpose SPLSs with dwell time are presented, and the relation between these conditions is illustrated. Some of these conditions are given in terms of infinite-dimensional linear programming (LP), which cannot be solved directly. Then, by utilising the piecewise linear approach, new alternative convex conditions are formulated in terms of finite-dimensional LP. Compared to the existing literature, results with lower or at least the same conservatism can be obtained under the new conditions for the same discretised order. An algorithm is given to reduce the computational cost. Meanwhile, it is proved that there exists a relation between these convex and non-convex conditions if the discretised order is sufficiently large. By utilising the transpose conditions, alternative convex conditions on stabilisation of SPLSs with dwell time are also presented. The controller gain matrices can be computed by solving a set of LP directly. Finally, the correctness and superiority of the results are verified by numerical examples.

Dwell time stability and stabilization of interval discrete-time switched positive linear systems

This paper investigates the dwell time stability and stabilization problems of discrete-time switched positive linear systems (DSPLSs) with interval uncertainties. The dwell time refers to constant dwell time, ranged dwell time and minimum dwell time. At first, some sufficient conditions are presented for the dwell time stability of primal and transpose interval DSPLSs. Meanwhile, the conservatisms of these conditions are compared. Then, equivalent stabilization conditions are presented for interval DSPLSs with dwell time. The controller gain matrices can be computed by solving the convex lifted conditions directly. All the results are given in terms of linear programming (LP). At last, several numerical examples verify the correctness and significance of the results.

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.

Distributed fault tolerant tracking control for large‐scale multi‐motor web‐winding systems

This study is concerned with the distributed fault tolerant tracking control for large-scale multi-motor web-winding systems. Firstly, the web-winding system is considered a synthetic system with several dynamic subsystems subject to multiple disturbances and actuator faults. Then, a disturbance compensation-based distributed fault diagnosis scheme is developed to estimate the system actuator faults. By setting the reference outputs, a method of obtaining equilibrium control inputs and equilibrium states is formulated to achieve the distributed variation dynamic model at equilibrium points by Taylor expansion. Based on the estimated actuator faults, an effective distributed fault tolerant control strategy is proposed by the techniques of interval matrix and disturbance local compensation. Sufficient conditions of asymptotic stability of the estimation error systems and the closed-loop systems are derived based on the Lyapunov theory. A fault diagnosis observer and a fault tolerant controller gain matrices are obtained by solving the linear matrix inequalities. Finally, simulations and analysis are performed on the three-motor web-winding system to verify the effectiveness of the proposed distributed fault tolerant control strategy.

Finite‐time asynchronous control for positive discrete‐time Markovian jump systems

Finite-time asynchronous control problem is discussed for positive Markovian jump systems in this study. The non-synchronous behaviours generated between the system modes and controller modes are fully considered. To ensure the closed-loop system positivity and finite-time boundedness with a guaranteed $H_\infty $H ∞ performance level, a sufficient condition on the existence of an asynchronous controller is first established by applying Lyapunov-Krasovskii functional approach and recursive matrix inequality methods. Then, with the aid of matrix conversions, the specific form of controller gain matrices can be constructed by solving linear matrix inequality (LMI) conditions. A numerical example is presented and application is illustrated to validate the proposed results by employing a pest's age-structured population dynamic model.

Relaxed Real-Time Scheduling Stabilization of Discrete-Time Takagi–Sugeno Fuzzy Systems via An Alterable-Weights-Based Ranking Switching Mechanism

The problem of relaxed real-time scheduling stabilization of nonlinear systems in the Takagi–Sugeno fuzzy model form is studied by proposing a new alterable-weights-based ranking switching mechanism. Thanks to the proposed alterable-weights-based ranking switching mechanism, a new fuzzy switching controller is developed with a set of activated modes that are adjusted by the real-time joint distribution of normalized fuzzy weighting functions. It is worth noting that those existing real-time scheduling stabilization results can be improved without introducing additional offline computational burden while solving control gain matrices. More importantly, less conservative stabilization conditions lead to a smaller degree of the fuzzy homogenous polynomially parameter-dependent switching controller, and thus, less online computational burden is required in the actual application. The effectiveness and superiority of the proposed method are verified by two simulation examples in the numerical section.

Dissipativity-Based Controller Design for Time-Delayed T-S Fuzzy Switched Distributed Parameter Systems

This paper studies fuzzy controller design problem for a class of nonlinear switched distributed parameter systems (DPSs) subject to time-varying delay. Initially, the original nonlinear DPSs are accurately described by Takagi-Sugeno fuzzy model in a local region. On the basis of parallel distributed compensation technique, mode-dependent fuzzy proportional and fuzzy proportional-spatial-derivative controllers are constructed, respectively. Subsequently, using single Lyapunov-Krasovskii functional and some matrix inequality methods, sufficient conditions that guarantee the stability and dissipativity of the closed-loop systems are presented in the form of linear matrix inequalities, which allow the control gain matrices to be easily obtained. Finally, numerical examples are provided to demonstrate the validity of the designed controllers.

Exponential synchronization of a Markovian jump complex dynamic network with piecewise-constant transition rates and distributed delay

The exponential synchronization of a Markovian jump complex dynamical network with piecewise-constant transition rates is investigated. Two distinct types of time-varying delay are considered for the system; one is distributed time-delay for each node, the other is discrete coupling time-delay. Based on an augmented Lyapunov–Krasovskii functional, some sufficient conditions are derived and expressed in the form of linear matrix inequalities, which are formulated in such a manner as to determine the controller gain matrices. Finally, an example is given to illustrate the effectiveness and validity of the proposed method.

Stability analysis and synthesis for switched Takagi–Sugeno fuzzy positive systems described by the Roesser model

This article focuses on stability analysis and controller synthesis of a class of Roesser-type switched Takagi–Sugeno fuzzy systems with delays. First, sufficient conditions derived by use of the co-positive Lyapunov function and the average dwell time method are presented to guarantee the proposed system is positive and exponentially stable. Then via a state feedback fuzzy controller, criteria are also given under which not only the resulting closed-loop system is positive and exponentially stable but also the desired controller gain matrices can be designed by solving a set of coupled matrix inequalities. Finally, two illustrative examples are provided to show the effectiveness of the approach outlined in this article.

Design of a H∞ model reference tracking control for interconnected nonlinear systems by decentralized dynamic output-feedback

This study investigates the problem of robust tracking control for interconnected nonlinear systems affected by uncertainties and external disturbances. The designed H∞ dynamic output-feedback model reference tracking controller is parameterized in terms of linear matrix inequalities (LMIs), which is formulated within a convex optimization problem readily implementable. The resolution of such a problem, guarantying not only the quadratic stability but also a prescribed performance level of the resulting closed-loop system, enables to calculate concurrently the robust decentralized control and observation gain matrices. The established LMI conditions are computed in a single-step resolution to obtain all the controller/observer parameters and therefore to overcome the problem of iterative algorithm based on a multi-stage resolution leading in most cases to conservative and suboptimal solutions. Numerical simulations on diverse applications ranging from a numerical academic example to coupled inverted double pendulums and a 3-strongly interconnected machine power system are provided to corroborate the merit of the proposed control scheme.

Dissipativity-based non-fragile sampled-data control design of interval type-2 fuzzy systems subject to random delays

This paper investigates the β-dissipativity-based reliable non-fragile sampled-data control problem for a class of interval type-2 (IT2) fuzzy systems. In particular, it is allowed to have randomly occurring time-varying delays in the controller design, which are modeled by Bernoulli distributed white noise sequences. Precisely, the IT2 fuzzy model and the non-fragile sampled-data controller are formulated by considering the mismatched membership functions. By constructing an appropriate Lyapunov–Krasovskii functional, a set of delay-dependent conditions is derived to guarantee that the closed-loop IT2 fuzzy system is strictly <Q,S,R>-β-dissipative. Moreover, the gain matrices of feedback reliable non-fragile sampled-data controller are derived in terms of linear matrix inequalities (LMIs), which can be solved by using existing LMI solvers. Two numerical examples are eventually given to illustrate the applicability and effectiveness of the proposed controller design technique.

Proportional integral observer-based decentralized stabilization design scheme for nonlinear complex interconnected systems

For a class of complex interconnected nonlinear disturbed systems, a proportional integral (PI) decentralized observer-based feedback robust decentralized controller technique is proposed, relying on H∞ synthesis for disturbance mitigation and linear matrix inequality (LMI) tools to achieve asymptotic stabilization and stability analysis within the Lyapunov framework. The proposed design method draws on a prominent optimization problem that can be tackled in terms of LMI constraints to evaluate the decentralized controller and PI observer gain matrices jointly, to maximize the nonlinearity coverage tolerated by the system without destabilization and to improve the robustness of the proposed control strategy by minimizing an H∞ criterion despite exogenous disturbances and strong nonlinear interconnections affecting the subsystems. The efficacy and high performance of the proposed control approach, compared with a renowned decentralized guaranteed cost control strategy from the literature, are validated by numerical simulations on a greatly interconnected three-machine power system.

Robust fuzzy tracking control of a quad-rotor unmanned aerial vehicle based on sector linearization and interval matrix approaches

In this paper, the robust H∞ fuzzy tracking control strategy for a quad-rotor unmanned aerial vehicle (UAV) with strong coupling and highly nonlinear is put forward based on the Takagi-Sugeno(T-S) fuzzy error model. Firstly, the quad-rotor UAV system is divided into altitude subsystem, position subsystem and attitude subsystem. Through selecting appropriate premise variables, three T-S fuzzy error models, which are equivalent to the error dynamic model, are established by the sector linearization approach. Next, the uncertainties in drag coefficients, moments of inertia are taken into account, and the interval matrix is introduced to describe them in altitude, position and attitude T-S fuzzy error models. Then the robust H∞ fuzzy feedback controllers are designed to stabilize T-S fuzzy subsystems. Besides, according to the Lyapunov stability theorem, it is obtained that the LMI sufficient conditions of exponential stability with the prescribed H∞ performance for T-S fuzzy closed-loop subsystems. Meanwhile, the method for solving the gain matrices of controller is presented. Finally, simulation results are given to demonstrate the effectiveness, robustness and advantages of the proposed method. Then the feasibility of the proposed method is further verified by experimental results.

Anti-windup control for nonlinear singularly perturbed switched systems with actuator saturation

ABSTRACTThis paper considers the problem of anti-windup (AW) control for nonlinear singularly perturbed switched systems with actuator saturation. An AW controller consisting of a dynamic state feedback (DSF) controller and an AW compensator is firstly constructed. Then, two methods are proposed to determine the AW controller gain matrices by a common Lyapunov function. One of which assumes that the singular perturbation parameter ϵ is available and designs ϵ-dependent AW controller gains simultaneously. The other one, which considers the case that ϵ is unknown but sufficiently small, designs the ϵ-independent DSF controller gain matrices first and then designs the ϵ-independent AW compensator gain matrices. Both of the methods are reduced to solving convex optimisation problems and can achieve larger stability bound and basin of attraction than the existing results. Finally, examples are used to illustrate the feasibility and advantages of the proposed methods.

Non-fragile controller design of uncertain saturated polynomial fuzzy systems subjected to persistent bounded disturbance

This paper investigates the problem of designing a non-fragile polynomial fuzzy controller for a class of polynomial fuzzy models subjected to persistent bounded disturbances and system uncertainty. The proposed controller is considered to satisfy the input saturation constraint. Furthermore, the resilient controller is affected by linear fractional uncertainties. The overall structure of the controller is obtained by the polynomial parallel distributed compensation concept. The sufficient conditions guarantee an L1 performance of the perturbed system and exponential stability of the non-perturbed system is achieved in terms of sum-of-squares decomposition conditions. Subsequently, the sum-of-squares-based conditions lead to minimization of the L1 performance such that the above-mentioned hard constraints on the control input and robustness of the closed-loop system against the system and controller uncertainties will be guaranteed. The controller gain matrices will be achieved by numerically solving the sum-of-squares-based conditions with the third-party MATLAB toolbox ‘SOSTOOLS’. Finally, extensive studies and hardware-in-the-loop simulations on a ball-and-beam system are presented, which illustrate the proposed controller can accurately and smoothly track the set point frequency. Furthermore, the proposed control approach is more robust over prior-art controllers for all the simulation scenarios.

Robust Observer-Based H∞ Controller Design for Motorcycle Lateral Dynamics

The present work deals with the design problem of a robust observer-based controller for a motorcycle system using LPV approach. The designed model is specifically uncertain and disturbed one, whose uncertainties are related to variations of both the cornering stiffness and the longitudinal velocity. The nonlinear motorcycle model is firstly transformed on an uncertain LPV model with two vertices; then an observer-based H∞ robust controller is designed. Both the controller and observer gain matrices are computed by solving a unified convex optimization problem under LMI constraints using YALMIP solver. Numerical simulation results are given to illustrate the effectiveness of the designed method.

Controller design for stochastic Markovian switching systems with time-varying delay and actuator saturation

ABSTRACTThe paper deals with controller design for stochastic Markovian switching systems with time-varying delay and actuator saturation by implying a new criterion for the domain of attraction firstly. By constructing more appropriate Lyapunov–Krasovskii functional, some new conditions for verifying stochastic stability of the plant are established. Then, the state feedback controller is designed to expand the domain of attraction of the corresponding closed-loop system. The procedure of deriving controller gain matrices is converted into an optimisation problem with constraints of a set of linear matrix inequalities. The mathematical model of RLC series circuit illustrates the validity of the obtained results.

Observer-Based Event-Triggered Control for Nonlinear Systems With Mixed Delays and Disturbances: The Input-to-State Stability.

In this paper, the input-to-state stabilization problem is investigated for a class of nonlinear delayed systems with exogenous disturbances. The model under consideration is general that covers for both mixed time-delays and Lipschitz-type nonlinearities. An observer-based controller is designed such that the closed-loop system is stable under an event-triggered mechanism. Two separate event-triggered strategies are proposed in sensor-to-observer (S/O) and controller-to-actuator (C/A) channels, respectively, in order to reduce the updating frequencies of the sensor and the controller with guaranteed performance requirements. The notion of input-to-state practical stability is introduced to characterize the performance of the controlled system that caters for the influence from both disturbances and event-triggered schemes. The estimates of the upper bounds of the delayed states and two measurement errors are employed to analyze and further exclude the Zeno behavior resulting from the proposed event-triggered schemes in S/O and C/A channels. The controller gain matrices and the event-trigger parameters are co-designed in terms of the feasibility of certain matrix inequalities. A numerical simulation example is provided to illustrate the effectiveness of theoretical results.

Resilient dynamic output feedback control for discrete-time descriptor switching Markov jump systems and its applications

This paper investigates the resilient dynamic output feedback (DOF) control problem for discrete-time descriptor switching Markov jump systems for the first time, where the time-varying transition probabilities are described by a piecewise-constant matrix and a high-level signal subject to average dwell time switching. The controllers to be designed can tolerate additive gain perturbations. Firstly, by constructing a stochastic Lyapunov functional and using an average dwell time method, a sufficient condition is given such that the resultant closed-loop systems are stochastically admissible and have a $$H_{\infty }$$ noise attenuation performance. Then, based on the matrix inequality decoupling technique, a novel linear matrix inequality (LMI) condition is presented such that the resultant closed-loop systems are stochastically admissible with a $$H_{\infty }$$ noise attenuation performance. When the uncertain parameters exist not only in plant matrices but also in controller gain matrices, the resilient DOF controller is developed in terms of LMIs, which can be of full order or reduced order. Compared with the previous ones, the proposed design methods do not impose extra constraints on system matrices or slack variables, which show less conservatism. Finally, numerical examples are given to illustrate the superiority and applicability of the new obtained methods.

Asynchronous L1-gain control of uncertain switched positive linear systems with dwell time

In this paper, dwell time (DT) stability, L1-gain performance analysis and asynchronous L1-gain controller design problems of uncertain switched positive linear systems (SPLSs) are investigated. Via a time-scheduled multiple linear co-positive Lyapunov function (TSMLCLF) approach, convex sufficient conditions of DT stability and L1-gain performance of SPLSs with interval and polytopic uncertainties are presented. Furthermore, by utilizing the feature that the TSMLCLF keeps decreasing even if the controller is running asynchronously with the system, the asynchronous L1-gain controller design problem of SPLSs with interval and polytopic uncertainties is investigated. Convex sufficient conditions of the existence of time-varying asynchronous state-feedback controller which can ensure the closed-loop system's positivity, stability and L1-gain performance are established, and the controller gain matrices can be calculated instantaneously online. The obtained L1-gain in the paper is standard. All the results are presented in terms of linear programming. A practical example is provided to show the effectiveness of the results.