Piecewise Lyapunov Function Method Research Articles

$$H_\infty $$ H ∞ switching synchronization for multiple time-delay chaotic systems subject to controller failure and its application to aperiodically intermittent control

This paper is concerned with the \(H_\infty \) synchronization control problem for a class of chaotic systems with multiple delays in the presence of controller temporary failure. Based on the idea of switching, the synchronization error systems with controller temporary failure are modeled as a class of switched synchronization error systems. Then, a switching condition that incorporates the controller failure time is constructed by using piecewise Lyapunov functional and average dwell-time methods, such that the switched synchronization error systems are exponentially stable and satisfy a weighted \(H_\infty \) performance level. In the meantime, a switching state feedback \(H_\infty \) controller is derived by solving a set of linear matrix inequalities. More incisively, the obtained results can also be applied to the issue of aperiodically intermittent control. Finally, three simulation examples are employed to illustrate the effectiveness and potential of the proposed method.

Observer-based periodically intermittent control for linear systems via piecewise Lyapunov function method

This paper focuses on the observer-based periodically intermittent control issue for linear systems by utilizing piecewise Lyapunov function method. Based on the concept of intermittent control, the description of an observer-based periodically intermittent controller is initially proposed. Then, stability of the corresponding periodically intermittent control system is analyzed by resorting to piecewise Lyapunov function method. Here, the so-called piecewise Lyapunov function means that Lyapunov function on control time intervals differs from the one on free time intervals. Besides, the existence of an observer-based periodically intermittent controller is converted into the feasibility of linear matrix inequalities. It is worth pointing out that, in comparison with an observer-based continuous controller, the designed observer-based periodically intermittent controller can still retain satisfactory performance with shorter control task execution time. Finally, an illustrative simulation example is given to show the validity and superiority of the result.

Control and resource allocation of cyber‐physical systems

The authors investigate the problem of control and channel resource allocation of a set of plants controlled by a remote computer in a cyber-physical system framework via a wireless network. Owing to capacity limitation, at any time only a subset of plants are allowed to be attended by the cyber controller while others must wait. To establish a promising scheduling policy regulating the allocation of the controller attention to the plants, they use binary sequences to model the allocation procedure. Taking advantage of the binary sequences and considering the packet loss effects in the channel, they establish sufficient conditions guaranteeing simultaneous stabilisation of the collection of systems. Most excitedly, a systematic methodology for the scheduling and controller co-design is established, which supplies a constructive and easily applicable design tool for most regular binary sequences and state-feedback controllers for the collection of plants. The theory and the results are built on the piecewise Lyapunov function method and the average dwell time techniques. A numerical example and laboratory experiment results are given to demonstrate the effectiveness of the binary sequences sequence-based co-design method.

Robust stabilisation and L2 -gain analysis for switched systems with actuator saturation under asynchronous switching

Robust stabilisation and L2-gain analysis for a class of switched systems with actuator saturation are studied in this paper. The switching signal of the controllers lags behind that of the system modes, which leads to the asynchronous switching between the candidate controllers and the subsystems. By combining the piecewise Lyapunov function method with the convex hull technique, sufficient conditions in terms of LMIs for the solvability of the robust stabilisation and weighted L2-gain problems are presented respectively under the dwell time scheme. Finally, a numerical example is given to demonstrate the feasibility and effectiveness of the proposed results.

Hybrid event-time-triggered networked control systems: Scheduling-event-control co-design

This paper is concerned with the simultaneous stabilization of a collection of plants remotely controlled via a wireless network. The so-called most regular binary sequences (MRBSs) are used to allocate the limited network channels. To further reduce unnecessary transmissions, an event-triggered transmitter is introduced at each plant. Under the hybrid event-time-triggered transmission strategy, a sufficient stability condition is derived for each plant. Then, a unified co-design framework is presented with which the scheduling functions (i.e., the MRBSs), the event-triggering condition and the controller gains can be determined simultaneously. The main results are established using piecewise Lyapunov functional method and average dwell time technique. The effectiveness of the co-design method is demonstrated by a numerical example.

Output Feedback Tracking Control for a Class of Switched Nonlinear Systems with Time-varying Delay

This paper studies the problem of tracking control for a class of switched nonlinear systems with time-varying delay. Based on the average dwell-time and piecewise Lyapunov functional methods, a new exponential stability criterion is obtained for the switched nonlinear systems. The designed output feedback H ? controller can be obtained by solving a set of linear matrix inequalities (LMIs). Moreover, the proposed method does not need that a common Lyapunov function exists for the switched systems, and the switching signal just depends on time. A simulation example is provided to demonstrate the effectiveness of the proposed design scheme.

Impulsive perturbations in a predator–prey model with dormancy of predators

In this paper, a predator–prey model consisting of active and dormant states of predators with impulsive control strategy is established. Using Floquet theories, the small amplitude perturbation technique and the piecewise Lyapunov function method, the conditions of local and global asymptotical orbital stability of the prey-eradication periodic solution are obtained. The boundness and permanence of the impulsive system are proved by the comparison principle. Through numerical simulations, the effects of the impulsive perturbation on the inherent oscillation are investigated, which implies that the impulsive perturbation can lead to period-doubling bifurcation, chaos, and period-halving bifurcation. Moreover, the effects of the impulsive perturbation and hatching rate on the chaos of the system are comparatively studied by numerical simulation. These obtained results can be useful for ecosystem management and for explaining complex phenomena of ecosystems.

Exponential stability of switched genetic regulatory networks with both stable and unstable subsystems

This paper concerns the stability analysis problem for stochastic delayed switched genetic regulatory networks (GRNs) with both stable and unstable subsystems. By employing the piecewise Lyapunov functional method combined with the average dwell time approach, we show that if the average dwell time is chosen sufficiently large and the derivative of the Lyapunov-like function for unstable subsystems is bounded by certain kind of continuous function, then exponential stability criteria of a desired degree are guaranteed. The derived results show that the minimal average dwell time is proportional to the time delays. Finally, an example is given to illustrate the effectiveness of the derived results.

Guaranteed Cost Control for Fuzzy Bilinear Systems with Uncertain Parameters

The main theme of this paper is to present robust guaranteed cost control laws for a class of fuzzy bilinear systems (FBS) with parametric uncertainties. First, the piecewise Lyapunov function (PLF) method is utilized to design a fuzzy controller, which ensures the robust asymptotic stability of the closed-loop system, and then the robust guaranteed cost control law is also proposed. Second, based on the Schur complement and some variable transformations, some sufficient conditions are derived to guarantee the stability of the overall fuzzy control system via linear matrix inequalities (LMIs). Finally, a numerical example is utilized to demonstrate the validity and effectiveness of the proposed control scheme.

Stability analysis for switched genetic regulatory networks: An average dwell time approach

In this correspondence, the problem of exponential stability for switched genetic regulatory networks (GRNs) with time delays is investigated. The GRNs are composed of N modes and the network switches from one mode to another. By employing the piecewise Lyapunov functional method combined with the average dwell time approach and by using a novel Lyapunov–Krasovskii functional (LKF), sufficient criteria are given to ensure the exponential stability for the switched GRNs with constant and time-varying delays, respectively. These criteria are proved to be much less conservative than the most recent results, since the results reported in this paper not only depend on the delay bounds, but also depend on the partitioning. All the conditions presented here are in the form of matrix inequalities which are easy to be verified via the Matlab toolbox. Two examples are provided in the end of this paper to illustrate the effectiveness of the obtained theoretical results.

Tracking control for switched time-varying delays systems with stabilizable and unstabilizable subsystems

We investigate the tracking control problem for switched linear time-varying delays systems with stabilizable and unstabilizable subsystems. Sufficient conditions for the solvability of the tracking control problem are developed. The tracking control problem of a switched time-varying delays system with stabilizable and unstabilizable subsystems is solvable if the stabilizable and unstabilizable subsystems satisfy certain conditions and admissible switching law among them. Average dwell time approach and piecewise Lyapunov functional methods are utilized to the stability analysis and controller design. By introducing the integral controllers and free weighting matrix scheme, some restricted assumptions imposing on the switched systems are avoided. A simulation example shows the effectiveness of the proposed method.

Controller Failure Analysis for Systems with Interval Time-Varying Delay: A Switched Method

This paper studies the problem of controller failure analysis for a class of interval time-varying delay systems with a predesigned state feedback controller. Our objective is to establish conditions concerning controller failure time, under which the systems still keep exponentially stable. For this purpose, the systems with controller failures are first formulated as a class of switched delay systems. Next, based on a piecewise Lyapunov functional method, the exponential stability of such systems is guaranteed by restricting the unavailable rate and failure frequency of the controller. All the results are presented in terms of linear matrix inequalities. Two examples are provided to demonstrate the effectiveness of the proposed technique.

Stability of Systems With Controller Failure and Time-Varying Delay

This paper studies the stability for a class of systems with time-varying delay subject to controller failure. It explores under what conditions of controller failure the system is still exponentially stable. The concept of controller failure frequency is introduced. First, the delay system with failed controller is modelled as a class of switched delay systems. Next, based on two lemmas developed in this paper and the piecewise Lyapunov functional method, sufficient conditions are provided to guarantee the exponential stability of the system when controller failure occurs, which is in terms of the solvability of a set of linear matrix inequalities (LMIs). Finally, an example of a networked control system is given to illustrate the effectiveness of the proposed method.

Robust tracking control for switched linear systems with time-varying delays

Robust tracking control for switched linear systems with time-varying delays is investigated. Sufficient conditions for the solvability of robust tracking control problem are developed. Average dwell-time approach and piecewise Lyapunov functional methods are utilised for the stability analysis and controller design, and with free weighting matrix scheme, switching control laws are obtained such that the weighted H∞ model reference robust tracking performance is satisfied. By using linear matrix inequalities, the controller design problem can be solved efficiently. A simulation example shows the effectiveness of the proposed switching control laws.

Robust Fuzzy Guaranteed Cost Controller Design via Piecewise Lyapunov Function Approach

This paper considers the problem of robust guaranteed cost controller design for a class of nonlinear systems subject to time-varying and norm-bounded uncertainties in both state and input matrices. The Takagi-Sugeno (T-S) fuzzy model is employed to approximate the uncertain nonlinear system. Then, two different design procedures of optimal robust guaranteed cost controller are developed by using parallel distributed compensation (PDC) scheme and piecewise Lyapunov function (PLF) approach, respectively. And it is shown that all solvability conditions for the above problem can be converted into a standard linear matrix inequality (LMI) problem. The final numerical example is given to illustrate the effectiveness of the design procedures. In addition, the results obtained by PLF method are relatively less conservative.