A variable gain impulsive observer for Lipschitz nonlinear systems with measurement noises

This paper investigates the variable gain impulsive observer design problem for Lipschitz nonlinear systems. It is assumed that the measurements are contaminated by noise and received by observer at aperiodic instants. To establish a tractable design condition for impulsive observers, the piecewise linear interpolation method is used to construct the variable gain function. To quantify the impact of the measurement noises and exogenous disturbance on the estimation error, a Lyapunov-based condition for establishing exponential input-to-state stability (EISS) property of the observation error dynamics is presented. Then it is shown that the EISS condition can be expressed as a set of linear matrix inequalities (LMIs) by introducing a piecewise quadratic Lyapunov function. A convex optimization problem is proposed in which the EISS gain is minimized. Comparisons with the existing methods show the effectiveness of the proposed design technique.     

Consensus for heterogeneous networked multi-agent systems with switching topology and time-varying delays

This paper investigates consensus problem for heterogeneous discrete linear time-invariant (LTI) multi-agent systems subjected to time-varying network communication delays and switching topology. A new two-stage consensus protocol is proposed based on stochastic, indecomposable and aperiodic (SIA) matrix and pseudo predictive scheme. With pseudo predictive scheme the network delay is compromised. Consensus analysis based on seminorm is provided. Results give conditions for such systems with periodic switching topology and time-varying delays to reach consensus. Highlights of the paper include: the protocol can be implemented in a distributed manner; the pseudo predictive approach requires less computation and communication; the verification of consensus convergence does not require the global information about the communication topology; the protocol allows delay to be time-varying, topology to dynamically and asymmetrically switch and system mode to be unstable. Numerical and practical examples demonstrate the effectiveness of the theoretical results.     

A delay-derivative-dependent approach to robust H∞ filter design for uncertain systems with time-varying distributed delays

This paper focuses on the problem of robust H∞ filter design for uncertain systems with time-varying state and distributed delays. System uncertainties are considered as norm-bounded time-varying parametric uncertainties. The delays are assumed to be time-varying delays being differentiable uniformly bounded with delay-derivative bounded by a constant, which may be greater than one. A new delay-derivative-dependent approach of filter design for the systems is proposed. A novel Lyapunov-Krasovskii functional (LKF) is employed, and a tighter upper bound of its derivative is obtained by employing an inequality and using free-weighting matrices technique, then the proposed result has advantages over some existing results, in that it has less conservatism and it enlarges the application scope. An improved sufficient condition for the existence of such a filter is established in terms of linear matrix inequality (LMI). Finally, illustrative examples are given to show the effectiveness and reduced conservatism of the proposed method.     

A compensator design technique for control systems with time-varying nonlinear elements

A method is advanced for the design of linear controllers for a class of nonlinear systems. The systems considered in this paper are characterized by the presence of a dominant nonlinearity located in a specified sector. The proposed approach is digital-computer oriented, and design results are presented in parameter planes and parameter space.     

A robust low-complexity tracker design with preassigned performance for uncertain high-order nonlinear systems with unknown time-varying delays and high powers

A robust low-complexity design methodology is presented for global tracking of uncertain high-order nonlinear systems with unknown time-varying delays. In contrast to the existing literature, this paper assumes that nonlinear bounding functions of time-delay nonlinearities and high powers of virtual and actual control variables are unknown. Furthermore, a delay-independent tracking scheme using nonlinearly transformed error surfaces is simply designed without the knowledge of nonlinear bounding functions of model nonlinearities, the adaptive technique, and the calculation of repeated time derivatives of certain signals. Thus, the proposed tracker is implemented with low complexity. It is recursively shown that the tracking error is preserved within the predefined bounds of transient and steady-state performance in the Lyapunov sense.     

Parameter-dependent finite-time observer design for time-varying polytopic uncertain switched systems

Mathematical models are an approximate of physical systems and design procedures are only complete when modeling errors have been quantified. Uncertainties are incorporated in design procedure to compensate such discrepancies and to add robustness. This paper investigates the design problem of parameter-dependent switched observers   for polytopic uncertain switched systems. State-space model is considered subject to time-varying uncertainties, and designated observer gains ensuring stability of overall system are also parameter-dependent. Synthesis procedure is demonstrated by employing _?∞${?}_{\infty }$ performance criteria which has become a standard for robust system design against external disturbances. This investigation is carried out in the framework of finite-time stability (FTS) and finite-time boundedness (FTB) which is the focus of researchers recently because of its apparent practical significance, especially after the emergent utilization of linear matrix inequalities.     

Dissipative state observer design for nonlinear time-delay systems

This paper is concerned with the design of dissipative state observers for a family of time-delay nonlinear systems. The Dissipativity method, proposed by one of the authors for delay-free nonlinear systems, is extended here to a class of time-delay nonlinear systems. The design method consists in decomposing the time-delay estimation error dynamics into a time-delay linear subsystem and a time-varying memoryless nonlinearity, connected in a negative feedback loop. By using some storage functionals, both delay-independent and delay-dependent dissipativity criteria are derived in order to guarantee the exponential convergence property of the observer. The exponential stability of the estimation error is then ensured, assuming that the nonlinearity is dissipative with respect to a quadratic supply rate and the linear part is designed, through the observer gains, to be dissipative with respect to a complementary supply rate. The design conditions are formulated in terms of tractable bilinear (BMI’s) or linear matrix inequalities (LMI’s). An interesting advantage is that the proposed dissipative design extends and generalizes under a unified framework several methods available in the literature, since a wide diversity of nonlinearities can be considered. Numerical examples are provided to demonstrate the effectiveness of the theoretical results.     

Event-triggered consensus of nonlinear multi-agent systems with stochastic switching topology

This paper is concerned with a leader-follower consensus problem for networked Lipschitz nonlinear multi-agent systems. An event-triggered consensus controller is developed with the consideration of discontinuous state feedback. To further enhance the robustness of the proposed controller, modeling uncertainty and switching topology are also considered in the stability analysis. Meanwhile, a time-delay equivalent approach is adopted to deal with the discrete-time control problem. Particularly, a sufficient condition for the stochastic stabilization of the networked multi-agent systems is proposed based on the Lyapunov functional method. Furthermore, an optimization algorithm is developed to derive the parameters of the controller. Finally, numerical simulation is conducted to demonstrate the effectiveness of the proposed control algorithm.     

Finite-time positiveness and distributed control of Lipschitz nonlinear multi-agent systems

The finite-time positiveness and distributed control problem is studied for a class of Lipschitz nonlinear multi-agent systems. The objective is to design a suitable distributed controller which makes the closed-loop multi-agent systems be positive and finite-time stabilizable and satisfy the given H_∞ performance index. Sufficient conditions are initially established on the existence of the finite-time distributed controller by using proper multiple Lyapunov functions and the design criteria are presented in the form of linear matrix inequalities. Finally, an example of multi-agent systems with six agents is presented to illustrate the feasibility and validity of the proposed methods.     

Event-triggered bipartite consensus for nonlinear multi-agent systems under switching topologies: A time-varying gain method

In this paper, the event-triggered bipartite consensus problem is investigated for nonlinear multi-agent systems under switching topologies, only part of topologies contain directed spanning tree rooted at the leader. First, a dynamic bipartite compensator is constructed based on relative output information to provide control signal. Then, the time-varying gain method is adopted to propose a compensator-based event-triggered control protocol without Zeno behavior. Notably, the control protocol proposed achieves the bipartite consensus while reducing update frequency effectively. Moreover, a low conservative switching law is designed by the topology-dependent average dwell time strategy, which fully considers the differences among topologies and provides an independent average dwell time for each topology. As an extension, the nonlinear multi-agent systems with non-zero input of leader are further studied. Finally, a practical example is presented to demonstrate the feasibility of proposed control protocol.     

EP-based adaptive tracker with observer and fault estimator for nonlinear time-varying sampled-data systems against actuator failures

An evolutionary programming-based adaptive observer is presented in this paper to improve the performance of state estimation of nonlinear time-varying sampled-data systems. Also, this paper presents a novel state-space adaptive tracker together with the proposed observer and estimation schemes for nonlinear time-varying sampled-data systems having actuator failures. For the class of slowly varying nonlinear time-varying systems, the proposed methodology is able to achieve the desired fault detection and performance recovery for the originally well-designed systems, as long as the controller having the high-gain property. For practical implementation, we utilize the advantages of digital redesign methodology to convert a well-designed high-gain analog controller/observer into its corresponding low-gain digital controller/observer. Illustrative examples are given to demonstrate the effectiveness of the proposed method. The developed digitally redesigned adaptive tracker with the proposed observer and estimator is suitable for implementation by using microprocessors.     

Stability criteria of a class of nonlinear impulsive switching systems with time-varying delays

This paper investigates stability problems of a class of nonlinear impulsive switching systems with time-varying delays. Based on the common Lyapunov function method and Razumikhin technique, several stability criteria are established for nonlinear impulsive switching systems with time-varying delays. Our results show that switching systems can be stabilized by impulsive switching signals even if the system matrices are all unstable. In the absence of impulses, some of our results reduce to similar stability criteria for nonimpulsive switching systems in some recent research articles. Several examples with simulations are given to illustrate the efficiency of our results.     

Impulsive observer design for a class of switched nonlinear systems with unknown inputs

This paper investigates hybrid observer design of a class of unknown input switched nonlinear systems. The distinguishing feature of the proposed method is that the stability of all subsystems of the error switched systems is not necessarily required. First, an output derivative-based method and time-varying coordinate transformation are considered to eliminate the unknown input. Then in order to maintain a satisfactory estimation performance, an impulsive full-order and switched reduced-order observer are developed with a pair of upper and lower dwell time bounds and constructing time-varying Lyapunov functions combined with convex combination technique. In addition, the time-varying Lyapunov functions method is also used to analyze the stability of a class of error switched nonlinear systems with stable subsystems. Finally, two examples are presented to demonstrate the effectiveness of the proposed method.     

Prescribed-time containment control of high-order nonlinear multi-agent systems based on distributed observer

This paper investigates the prescribed-time containment control problem for multi-agent systems with high-order nonlinear dynamics under a directed communication topology. Firstly, in view of the fact that only some follower agents can directly access the state information of multiple leader agents, a prescribed-time distributed observer is put forward to estimate the convex hull spanned by these leaders. Then, with the help of the distributed observer, a novel containment control method is developed for each follower based on a time-varying scaling function, so that all followers can converge to the convex hull spanned by the states of multiple leaders within a prescribed time. The comparison with the finite-time and fixed-time control methods differs in that the convergence time of the method proposed in this paper is independent of the initial conditions and control parameters and can be arbitrarily preassigned according to actual needs. Finally, an example is given to demonstrate the usefulness of the prescribed-time containment control method.     

Discrete-time nonlinear observer design with general criteria

A class of discrete-time nonlinear system and measurement equations having incrementally conic nonlinearities and finite energy disturbances is considered. A linear matrix inequality-based design approach is presented, which guarantees the satisfaction of a variety of performance criteria ranging from simple estimation error boundedness to dissipativity. Some simulation examples are included to illustrate and provide support to the proposed design methodology.     

Quadratic stability analysis and robust distributed controllers design for uncertain spatially interconnected systems

This paper is concerned with the quadratic stability analysis and robust distributed controllers design of both continuous-time and discrete-time uncertain spatially interconnected systems (USISs), where uncertainties are modeled by linear fractional transformation (LFT). The well-posedness, quadratic stability, and contractiveness of USISs are properly defined for the first time. A sufficient condition employing the given system matrices is established to check the well-posedness, quadratic stability and contractiveness. This condition is simpler than the existing conditions based on the decomposition of system matrices. Based on the new condition derived, a sufficient condition is given for the existence of robust distributed controllers and a constructive method is then presented for the design of robust distributed controllers. The advantage of the proposed constructive approach is that it employs the given system matrices while the existing methods conduct the bilinear transformation on these matrices when design controllers, and consequently, the constructive approach in this paper is computationally more efficient than the existing methods. Several examples are included to demonstrate the simplicity, efficiency and applicability of the derived theoretical results.     

An LMI approach to robust H∞ filtering for uncertain systems with time-varying distributed delays

In this paper, the problem of robust H_∞ filtering for uncertain systems with time-varying distributed delays is considered. The uncertainties under discussion are time varying but norm bounded. Based on the Lyapunov stability theory, sufficient condition for the existence of full order H_∞ filters is proposed by linear matrix inequality (LMI) approach such that the filtering error system is asymptotically sable and satisfies a prescribed attenuation level of noise. A numerical example is given to demonstrate the availability of the proposed method.