H∞ bumpless transfer for switched LPV systems and its application

In this paper, the approach of the control bumps limitation is generalised and applied to the problem of H _∞ bumpless transfer for a class of switched linear parameter-varying (LPV) systems. The H _∞ bumpless transfer problem is to design a controller with the amplitude limitation and a parameter and modes-dependent switching law to reduce control bumps of the switched LPV systems and satisfy an H _∞ performance index. The key point is to guarantee the bumps limitation constraint of the switched LPV systems by dual design of controllers and a switching law, even though the constraint for each subsystem is unsatisfied. First, a set of switching signals depending on parameters and modes are designed, and a family of switched LPV controllers with the bumps limitation objective are developed via multiple parameter-dependent Lyapunov functions. Then, a sufficient condition ensuring the H _∞ bumpless transfer performance for a switched LPV system is presented in the format of numerically tractable conditions. Finally, the effectiveness of the proposed control design scheme is illustrated by its application to the control design of an aero-engine.     

Robust H ∞ sliding mode control for a class of uncertain switched delay systems

This article considers the robust H _∞ sliding mode control problem for a class of uncertain switched delay systems. A single sliding surface is constructed such that the reduced-order equivalent sliding motion restricted to the sliding surface is completely invariant to all admissible uncertainties. For cases of known delay and unknown delay, the existence conditions of the sliding surface are proposed, respectively. The corresponding hysteresis switching laws are designed such that the sliding motion is stabilisable with H _∞ disturbance attenuation level γ. Furthermore, variable structure controllers are developed to drive the state of the switched system to reach the single sliding surface in finite time and remain on it thereafter. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design methods.     

Observer-based robust H-infinity control for uncertain switched systems

The problem of observer-based robust H-infinity control is addressed for a class of linear discrete-time switched systems with time-varying norm-bounded uncertainties by using switched Lyapunov function method. None of the individual subsystems is assumed to be robustly H-infinity solvable. A novel switched Lypunov function matrix with diagonal-block form is devised to overcome the difficulties in designing switching laws. For robust H-infinity stability analysis, two linear-matrix-inequality-based sufficient conditions are derived by only using the smallest region function strategy if some parameters are preselected. Then, the robust H-infinity control synthesis is studied using a switching state feedback and an observer-based switching dynamical output feedback. All the switching laws are simultaneously constructively designed. Finally, a simulation example is given to illustrate the validity of the results.     

Robust H ∞ control for a class of uncertain mechanical systems

In this article, the problem of H _∞ control is investigated for a class of mechanical systems with input delay and parameter uncertainties which appear in all the mass, damping and stiffness matrices. Two approaches, norm-bounded and linear fractional transformation (LFT) uncertainty formulations, are considered. By using a new Lyapunov–Krasovskii functional approach, combined with the advanced techniques for achieving delay dependence, improved robust H _∞ state-feedback controller design methods are developed. The existence condition for admissible controllers is formulated in the form of linear matrix inequalities (LMIs), and the controller design is cast into a convex optimisation problem subject to LMI constraints. If the optimisation problem is solvable, a desired controller can be readily constructed. The result for the norm-bounded uncertainty case improves the existing ones in terms of design conservatism, and that for the LFT uncertainty case represents the first attempt in this direction. An illustrative example is provided to show the effectiveness and advantage of the proposed controller design methodologies.     

Robust control for a class of uncertain switched fuzzy systems

A model of uncertain switched fuzzy systems whose subsystems are uncertain fuzzy systems is presented. Robust controllers for a class of switched fuzzy systems are designed by using the Lyapunov function method. Stability conditions for global asymptotic stability are developed and a switching strategy is proposed. An example shows the effectiveness of the method.     

Observer-based H ∞ control for networked systems with consecutive packet delays and losses

This paper considers the control problem for networked control systems (NCSs) with unreliable data communication. The unreliable data communication simultaneously exists in both control channel (from controller to actuator) and measurement channel (from sensor to controller) and may cause consecutive packet delays and losses. A new model is established based on all possible consecutive packet delays and losses. The observer-based controller is designed to exponentially stabilize the networked system in the sense of mean square, and also achieve the prescribed H _∞ disturbance attenuation level. An iterative algorithm is developed to compute the optimal H _∞ disturbance attenuation and the controller parameters by solving the semi-definite programming problem via interior-point approach. An illustrative example is provided to show the applicability of the proposed method.     

Event-triggered robust H∞ control for uncertain switched linear systems

In this paper, an event-triggering scheme is implemented in uncertain switched linear systems with time-varying delays and exogenous disturbance. Instead of standard periodically time-triggered, sampled-data control systems, the event-triggered control systems sample data only when an event, typically defined as some performance error exceeding a tolerant bound, occurs. Specifically, considering the disturbance existing in the system, the event-triggered robust H_∞ control problem is studied. In order to guarantee the robust H_∞ performance, the event-triggered full state feedback control, multiple Lyapunov functions method and state-dependent switching law are utilised to construct sufficient conditions in terms of linear matrix inequalities. In particular, since the event-triggered signals and switching signals may interlace with each other, the influence from them on the analysis of robust H_∞ performance is clarified. Subsequently, sufficient design conditions of the sub-controllers’ gains are further presented. Moreover, the Zeno problem is discussed to exclude continuously triggering and sampling. Finally, numerical simulations are provided to verify the feasibility of the proposed approach.     

Mixed H∞ and passive control for linear switched systems via hybrid control approach

This paper investigates the mixed H_∞ and passive control problem for linear switched systems based on a hybrid control strategy. To solve this problem, first, a new performance index is proposed. This performance index can be viewed as the mixed weighted H_∞ and passivity performance. Then, the hybrid controllers are used to stabilise the switched systems. The hybrid controllers consist of dynamic output-feedback controllers for every subsystem and state updating controllers at the switching instant. The design of state updating controllers not only depends on the pre-switching subsystem and the post-switching subsystem, but also depends on the measurable output signal. The hybrid controllers proposed in this paper can include some existing ones as special cases. Combine the multiple Lyapunov functions approach with the average dwell time technique, new sufficient conditions are obtained. Under the new conditions, the closed-loop linear switched systems are globally uniformly asymptotically stable with a mixed H_∞ and passivity performance index. Moreover, the desired hybrid controllers can be constructed by solving a set of linear matrix inequalities. Finally, a numerical example and a practical example are given.     

H ∞ output-feedback LPV control for systems with input saturation

This paper investigates the problem of designing a dynamic H _∞ output-feedback controller under an L _∞ performance representing componentwise input constraints. In order to derive a less conservative stabilization condition therein, this paper introduces a Lyapunov function-based polytopic control law and proposes a method capable of applying the information on interpolation parameters appearing in the procedure of representing saturation nonlinearity as convex polytope. Through this paper, the resultant H _∞/L _∞ problem is efficiently solved based on the set invariance condition formulated in terms of linear matrix inequalities (LMIs).     

Passivity and H∞ control of switched discrete-time nonlinear systems using linearisation

Local passivity and H_∞ control of switched discrete-time nonlinear systems are studied using the linearisation technique in this paper. We first establish LMI-based sufficient conditions under which theconsidered system is locally strictly QSR-dissipative. Then, two special cases of QSR-dissipativity, local passivity and l₂ gain, are investigated. In view of the derived conditions being all convex in linearised system matrices, local feedback passification and H_∞ control problems of switched discrete-time nonlinear systems are solved. The efficiency of the proposed method is verified through numerical examples.     

Residual mode filters and H ∞ control for a class of infinite-dimensional discrete-time systems

An H _∞, control problem with measurement feedback.for infinite-dimensional discrete-time (IDDT) systems whose homogeneous parts are described by Riesz-spectra operators is considered. The aim is to construct a finite-dimensional stabilizing controller for the IDDT system that makes the H _∞ norm of the closed-loop transfer function less than a given positive number δ. For that purpose, we first formulate the IDDT system as an IDDT system in l² and derive a finite-dimensional reduced-order system for the IDDT system in l². A stabilizing controller that makes the H _∞ norm of the closed-loop transfer function less than another positive number is then constructed for the reduced-order model. The finite-dimensional controller together with a residual mode Jilter plays a role of a finite-dimensional stabilizing controller that makes the H _∞ norm of the closed-loop transfer function less than δ for the original IDDT system, if the order of the residual mode filter is chosen suficiently large.     

H∞ control of a class of 2-D continuous switched delayed systems via state-dependent switching

This paper addresses the problem of state feedback H_∞ stabilisation of 2-D (two-dimensional) continuous switched state delayed systems represented by the Roesser model using the multiple Lyapunov functional approach. First, an asymptotical stability condition of 2-D continuous switched systems with state-dependent switching is derived. Second, a sufficient condition for H_∞ performance of the underlying system is established. Third, a state feedback controller is proposed to ensure that the resulting closed-loop system has a prescribed H_∞ performance level under a state-dependent switching signal. All the results are developed in terms of linear matrix inequalities. Finally, three examples are provided to demonstrate the validity and effectiveness of the proposed method.     

Design of finite-time H∞ controller for uncertain nonlinear systems and its application

This paper studies the problem of finite-time H _∞ control for strict feedback nonlinear systems with external disturbance. The finite-time stability theory, H _∞ control method, backstepping technique, together with adding a power integrator tool are combined to design a finite-time H _∞ state feedback controller. The obtained controller can make the closed-loop system finite-time convergent, and the influence of the external disturbance is attenuated to a given degree. Two numerical examples are presented to show the effectiveness and feasibility of the proposed method. Meanwhile, the proposed method is also applied to robot manipulators.     

Sojourn-probability-dependent H∞ control for networked switched systems under asynchronous switching

This paper considers H_∞ controller design for a class of networked switched discrete systems under asynchronous switching. The sojourn probability information – the probability of the switched systems staying in each subsystem – is first used to rebuild the networked switched systems. Also, a time-varying lag, depending on both the network-induced delays and switching signals, is taken into consideration between the switching instants of the controllers and systems model. By considering both sojourn probability information and asynchronous switching, a new kind of networked switched system model is proposed, wherein a set of random variables are proposed to describe the sojourn probabilities of the subsystems. Then, stability analysis and H_∞ performance analysis under asynchronous switching are derived. It should be noted that the system performance depends not only on the time-varying lag, but also on the sojourn probabilities. Finally, an example is given to illustrate the effectiveness of the proposed approach.