Robust reliable control design for networked control system with sampling communication

In this article, the problem of robust exponential stability and reliable stabilisation for a class of continuous-time networked control systems (NCSs) with a sample-data controller and unknown time-varying sampling rate is considered. The analysis is based on average dwell-time, Lyapunov–Krasovskii functional and linear matrix inequality (LMI) technique. The delay-dependent criteria are developed for ensuring the robust exponential stability of the considered NCSs. The obtained conditions are formulated in terms of LMIs that can easily be solved by using standard software packages. Furthermore, the result is extended to study the robust stabilisation for NCS with parameter uncertainties. A state feedback controller is constructed in terms of the solution to a set of LMIs, which guarantee the robust exponential stabilisation of NCS and the controller. Finally, numerical examples are presented to illustrate the effectiveness of the obtained results.     

An improved stability test and stabilisation of linear time-varying systems governed by second-order vector differential equations

In this article, the problems of exponential stability analysis and stabilisation of linear time-varying systems described by a class of second-order vector differential equations are considered. Using bounding techniques on the trajectories of a linear time-varying system, the stability problem of the time-varying system is transformed to that of a time-invariant system and a new sufficient condition for the exponential stability is obtained. Moreover, the new criterion is proven to be superior to a test presented in the recent literature. Finally, the proposed criterion is applied to the exponential stabilisation problem via state feedback. The results are illustrated by several numerical examples.     

Exponential stabilisation of memristive neural networks under intermittent output feedback control

In this paper, the exponential stabilisation problem is studied for a general class of memristive time-varying delayed neural networks under periodically intermittent output feedback control. First, the periodically intermittent output feedback control rule is designed for the exponential stabilisation of the memristive time-varying delayed neural networks. Then, we derive stabilisation criteria so that the memristive time-varying delayed neural networks are exponentially stable. By the mathematical induction method and constructing suitable Lyapunov–Krasovskii functionals, some easy-to-check criteria are obtained to ensure the exponential stabilisation of memristive time-varying delayed neural networks. Finally, two numerical simulation examples are given to illustrate the validity of the obtained results.     

Global exponential stabilisation of a class of nonlinear time-delay systems

This paper deals with the state and output feedback stabilisation problems for a family of nonlinear time-delay systems satisfying some relaxed triangular-type condition. The delay is supposed to be constant. Parameter-dependent control laws are used to compensate for the nonlinearities. Based on the Lyapunov–Krasovskii functionals, global exponential stability of the closed-loop systems is achieved. Finally, an extension to nonlinear time-varying delay systems is given.     

Exponential stabilisation of nonlinear parameter-varying systems with applications to conversion flight control of a tilt rotor aircraft

The exponential stabilisation problem of nonlinear parameter-varying (NPV) systems with input constraints is investigated. Unlike the existing NPV-related works, this paper directly addresses NPV models to conduct the stabilisation problem, without hiding nonlinearities or ignoring the time-varying nature. Existence conditions of a nonlinear time-varying (NTV) controller to render the uniformly exponential stability of an NPV system are given in terms of state-and-parameter-dependent linear matrix inequalities (SPLMIs). Specifically, a new controller structure and a novel Lyapunov functional are adopted such that the exact variation rates of the state and parameters can be incorporated into the SPLMIs. The generalised S-procedure is used to convexify the input constraints such that the resulting closed-loop system satisfies input constraints for any state starting from an admissible set. The derived SPLMIs can then be efficiently solved via sum-of-squares programming. The proposed approach is applied to the conversion flight control of a tilt rotor aircraft.     

Robust reliable sampled-data control for switched systems with application to flight control

This paper addresses the robust reliable stabilisation problem for a class of uncertain switched systems with random delays and norm bounded uncertainties. The main aim of this paper is to obtain the reliable robust sampled-data control design which involves random time delay with an appropriate gain control matrix for achieving the robust exponential stabilisation for uncertain switched system against actuator failures. In particular, the involved delays are assumed to be randomly time-varying which obeys certain mutually uncorrelated Bernoulli distributed white noise sequences. By constructing an appropriate Lyapunov–Krasovskii functional (LKF) and employing an average-dwell time approach, a new set of criteria is derived for ensuring the robust exponential stability of the closed-loop switched system. More precisely, the Schur complement and Jensen's integral inequality are used in derivation of stabilisation criteria. By considering the relationship among the random time-varying delay and its lower and upper bounds, a new set of sufficient condition is established for the existence of reliable robust sampled-data control in terms of solution to linear matrix inequalities (LMIs). Finally, an illustrative example based on the F-18 aircraft model is provided to show the effectiveness of the proposed design procedures.     

Sum-of-squares-based fuzzy controller design using quantum-inspired evolutionary algorithm

In the field of fuzzy control, control gains are obtained by solving stabilisation conditions in linear-matrix-inequality-based Takagi–Sugeno fuzzy control method and sum-of-squares-based polynomial fuzzy control method. However, the optimal performance requirements are not considered under those stabilisation conditions. In order to handle specific performance problems, this paper proposes a novel design procedure with regard to polynomial fuzzy controllers using quantum-inspired evolutionary algorithms. The first contribution of this paper is a combination of polynomial fuzzy control and quantum-inspired evolutionary algorithms to undertake an optimal performance controller design. The second contribution is the proposed stability condition derived from the polynomial Lyapunov function. The proposed design approach is dissimilar to the traditional approach, in which control gains are obtained by solving the stabilisation conditions. The first step of the controller design uses the quantum-inspired evolutionary algorithms to determine the control gains with the best performance. Then, the stability of the closed-loop system is analysed under the proposed stability conditions. To illustrate effectiveness and validity, the problem of balancing and the up-swing of an inverted pendulum on a cart is used.     

Input–output finite-time mean square stabilisation of stochastic systems with Markovian jump

The notion of input–output finite-time mean square (IO-FTMS) stability is introduced for Itô-type stochastic systems with Markovian jump parameters. Concerning a class of random input signals W, sufficient conditions are presented for the IO-FTMS stability and stabilisation of stochastic nonlinear Markov jump systems in terms of coupled Hamilton–Jacobi inequalities. When specialising to the linear case, these criteria are turned into coupled linear matrix inequalities. Moreover, the quadratic IO-FTMS stabilisation is addressed when polytopic uncertainty appears in the transition rate. Finally, a numerical example with simulations is exploited to illustrate the proposed techniques.     

An analysis and design for time-varying structures dynamical networks via state constraint impulsive control

This paper investigates the problems of exponential stabilisation criterion for time-varying structures dynamical networks via state constraint impulsive control. Two types of state constraint impulsive control schemes are proposed which include fully state constraint and partial state constraint. Combining with convex analysis, inductive method and matrix measure theory, some sufficient conditions are obtained to ensure exponential stabilisation for time-varying structures dynamical systems by using the constrains linear feedback impulsive controllers. Meanwhile, some simulation results are given to validate the effectiveness of the proposed criteria in the end.     

ℋ∞ stabilisation of switched linear stochastic systems under dwell time constraints

Based on the determination of a minimum dwell time, this article addresses the problem of characterising a switching strategy for ?_∞ stabilisation of switched linear stochastic systems with adapted external inputs. Sufficient conditions that assure exponential mean square stability and an ?_∞ performance index are established by analysing the time evolution of the second-order moment of the state and a recursive dynamic programming inequality, respectively. Alternative conditions are derived for numerical implementations. The proposed method is illustrated by numerical simulations.     

Delay-dependent robust stabilisation for a class of fuzzy bilinear systems with time-varying delays in state and control input

The stabilisation problem for a class of Takagi–Sugeno (TS) fuzzy bilinear systems (FBSs) with time-varying state and input delays is investigated in this article. A fuzzy controller is designed to stabilise TS FBSs with time-varying state and input delays via the parallel distributed compensation method. Based on a Lyapunov–Krasoviskii function, the delay-dependent stabilisation conditions are proposed in terms of a linear matrix inequality to guarantee the asymptotic stabilisation of time-delay FBSs with disturbance input. Two numerical examples with delays in the state and input are given to demonstrate that the proposed stability condition is less conservative than some existing results. Finally, the validity and applicability of the proposed control scheme are successfully demonstrated in the control of a Van de Vusse reactor with delay.     

Further results on global stabilisation and tracking control for underactuated surface vessels with non-diagonal inertia and damping matrices

This paper studies the global uniform stabilisation and exponential tracking problems for an underactuated ship with non-diagonal inertia and damping matrices. For the synthesis of the controller, first, the underactuated ship in question is converted into two cascade connected subsystems by using state and input transformations. Two constructive backstepping design schemes are developed, respectively, to get around the stabilisation burden and tracking burden. Along the way of proving stability analysis, it is shown that the designed control strategies can guarantee the global uniform asymptotic convergence of the state to the origin and global exponential convergence to the desired reference trajectory. Simulation results are provided to demonstrate the effectiveness of the proposed control methodologies.     

Robust stability analysis and stabilisation of uncertain impulsive positive systems with time delay

This paper considers the robust stability and stabilisation of uncertain impulsive positive systems with delay in state. The robust global exponential stability criterion under ranged dwell-time is first established by employing an impulse-time-dependent copositive Lyapunov function. Extensions to the exponential stability of the considered system under constant, arbitrary, maximal and minimal dwell-time are then derived. To positively stabilise the considered system under ranged dwell-time, a method of state-feedback controller design is presented based on the derived stability condition. Several numerical examples illustrate the reduced conservatism and effectiveness of the obtained theoretical results.     

Stabilisation of unstable FOPDT processes with a single zero by fractional-order controllers

In this article, stabilisation of unstable first-order-plus-dead-time (FOPDT) processes with a single zero by fractional-order (FO) controllers is investigated. A Nyquist stability criterion-based approach is adopted to derive the conditions for stability. Sufficient stabilisability conditions by FO [proportional integral] controllers and FO-lead–lag controllers are established. In addition, robust stability of the system with these FO controllers is investigated. To illustrate the results, some examples are provided.     

Lagrange stabilisation for uncertain phase-controlled systems

In this article, we are concerned with the Lagrange stabilisation problem for phase-controlled systems with parameter uncertainties. By using the Kalman–Yakubovich–Popov lemma, the frequency-domain conditions for Lagrange stability of nominal phase-controlled systems are converted into linear matrix inequality (LMI) conditions. The allowable parameter uncertainty bounds for controllability and observability, as well as LMI conditions for Lagrange stability of uncertain phase-controlled systems, are presented. A controller design strategy based on the LMI method is proposed such that the uncertain phase-controlled systems are Lagrange stabilised. A numerical example is provided to demonstrate the effectiveness of the proposed results.     

New delay-dependent conditions on robust stability and stabilisation for discrete-time systems with time-delay

This article is concerned with new robust stability conditions and robust stabilisation method for a discrete-time system with time-delay and time-varying structured uncertainties that come into state and input matrices. An improved approach to obtain new robust stability conditions is proposed. Our approach employs a generalised Lyapunov functional combined with the parameterised model transformation method and the generalised free weighting matrix method. These generalisations lead to generalised robust stability conditions that are given in terms of linear matrix inequalities. Moreover, based on new robust stability conditions, a robust stabilisation method for uncertain discrete-time systems with time-delay is given. Numerical examples compare our robust stability conditions with some existing conditions to show the effectiveness of our approach and also illustrate the improvement of our robust stabilisation method.     

Stabilisation of stochastic coupled systems via feedback control based on discrete-time state observations

This paper is concerned with the stabilisation of stochastic coupled systems (SCSs) via feedback control based on discrete-time state observations. State feedback control based on discrete-time observations is designed in the drift parts of the SCSs. Based on graph theory and Lyapunov method, the upper bound of the duration between two consecutive state observations is obtained. And a systematic method is given to construct a global Lyapunov function for SCSs via feedback control based on discrete-time state observations. A Lyapunov-type theorem and a coefficient-type criterion are obtained to guarantee the stabilisation in the sense of mean-square asymptotical stability and mean-square exponential stability. Furthermore, we use the theoretical results to analyse the stabilisation of stochastic coupled oscillators. Finally, we give a numerical example to illustrate the effectiveness and feasibility of the developed theoretical results.     

Exponential stabilisation for time-varying delay system with actuator faults: an average dwell time method

The issue of exponential stabilisation for a class of special time-varying delay switched systems resulting from actuator faults is considered in this article. The time-varying delay is assumed to belong to an interval and can be a slow or fast time-varying function. A hybrid state feedback strategy is redesigned to guarantee the system stable since the original controller is unavailable for some actuators failures. A class of switching laws incorporating the average dwell time method is proposed so that the special switched system with interval time-varying delay is exponentially stable. New delay-range-dependent stabilisation conditions using state feedback controllers are formulated in terms of linear matrix inequalities (LMIs) by choosing appropriate Lyapunov–Krasovskii functional without neglecting some useful knowledge on system states. Parameterised characterisations of the controllers are given in terms of the feasibility solutions to the LMIs. Two numeral examples are given to demonstrate the applicability and the effectiveness of the proposed method.