Junwei Lu

Passivity-based control for uncertain stochastic jumping systems with mode-dependent round-trip time delays

This paper considers the passivity-based control problem for stochastic jumping systems with mode-dependent round-trip time-varying delays and norm-bounded parametric uncertainties. By utilizing a novel Markovian switching Lyapunov functional, a delay-dependent passivity condition is obtained. Then, based on the derived passivity condition, a desired Markovian switching dynamic output feedback controller is designed, which ensures the resulting closed-loop system is passive. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed results.

Design of observers for a class of discrete-time uncertain nonlinear systems with time delay☆

This paper is concerned with the problem of observer design for a class of discrete-time Lipschitz nonlinear state delayed systems with, or without parameter uncertainty. The nonlinearities are assumed to appear in both the state and measured output equations. For both the cases with and without norm-bounded time-varying parameter uncertainties, a design method is proposed, which involves solving a linear matrix inequality (LMI). When a certain LMI is satisfied, the explicit expression of a desired nonlinear observer is also presented. An example is provided to demonstrate the applicability of the proposed approach.

Exponential dynamic output feedback controller design for stochastic neutral systems with distributed delays

This paper investigates the problem of stochastic stabilization for stochastic neutral systems with distributed delays. The time delay is assumed to appear in both the state and measurement equations. Attention is focused on the design of linear dynamic output feedback controllers such that the resulting closed-loop system is exponentially mean-square stable. A sufficient condition for the solvability of the problem is obtained in terms of a linear matrix inequality (LMI). When this LMI is feasible, an explicit expression of a desired dynamic output feedback controller is also given. The theory developed in this paper is demonstrated via a numerical example

Robust H∞ control for a class of uncertain nonlinear two-dimensional systems with state delays☆

Abstract This paper considers the problem of robust H ∞ control for uncertain 2-D discrete state-delayed systems in the Fornasini–Marchesini second local state-space model with a class of generalized Lipschitz nonlinearities. The parameter uncertainty is assumed to be norm-bounded. The problem to be addressed is the design of state feedback controllers such that the stability of the resulting closed-loop system is guaranteed and a prescribed H ∞ performance level is ensured for all admissible uncertainties. In terms of a linear matrix inequality (LMI), a sufficient condition for the solvability of the problem is obtained. A desired state feedback controller can be constructed by solving a certain LMI. A numerical example is provided to demonstrate the application of the proposed method.

Hopf bifurcation analysis of a complex-valued neural network model with discrete and distributed delays

In this paper, a class of complex-valued neural network model with discrete and distributed delays is proposed. Regarding the discrete time delay as the bifurcating parameter, the problem of Hopf bifurcation in the newly-proposed complex-valued neural network model is investigated under the assumption that the activation function can be separated into its real and imaginary parts. Based on the normal form theory and center manifold theorem, some sufficient conditions which determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are established. Finally, a numerical example is given to illustrate the validity of the theoretical results.

Design of fuzzy state feedback controller for robust stabilization of uncertain fractional-order chaotic systems

Abstract In this paper, the stabilization problem of uncertain fractional-order chaotic systems is investigated in the case where the fractional order α satisfies 0 α 1 and 1 ≤ α 2 . Firstly, the uncertain fractional-order chaotic system is described by the so-called fractional-order T–S fuzzy model, and then the fuzzy state feedback controller is correspondingly designed. Secondly, sufficient conditions are derived for the robust asymptotical stability of the closed-loop control systems in those two cases. These criteria are expressed in terms of linear matrix inequalities (LMIs), and the feedback gain matrices can be formulated into the solvability of the relevant LMIs. The proposed controller overcomes some defects in traditional control techniques and is easy to implement. Finally, two numerical examples are presented to demonstrate the effectiveness and the feasibility of the robust stabilizing controller and the robust asymptotical stability criteria.

Couple-group consensus for multi-agent networks of agents with discrete-time second-order dynamics

Abstract This paper considers the couple-group consensus problem for multi-agent networks with fixed and directed communication topology, where all agents are described by discrete-time second-order dynamics. Consensus protocol is designed such that some agents in a network reach a consistent value, while other agents reach another consistent value. The convergence of the system matrix is discussed based on the tools from matrix theory. An algebraic condition is established to guarantee couple-group consensus. Moreover, for a given communication topology, a theorem is derived on how to select proper control parameters and sampling period for couple-group consensus to be reached. Finally, simulation examples are presented to validate the effectiveness of the theoretical results.

Adaptive tracking control for uncertain switched stochastic nonlinear pure-feedback systems with unknown backlash-like hysteresis

Abstract In this paper, an adaptive tracking control problem is studied for a class of switched stochastic nonlinear pure-feedback systems with unknown backlash-like hysteresis under arbitrary switching. The mean-value theorem is used to overcome the difficulty arising from the pure-feedback structure. Based on neural networks’ approximation capability, an adaptive tracking control approach is developed via the adaptive backstepping technique and common Lyapunov function method. It is proved that the proposed control scheme can guarantee that all signals in the closed-loop system are semi-globally uniformly ultimately bounded in probability and the tracking error converges to an adjustable neighborhood of the origin. Finally, a simulation example further shows the effectiveness of the presented control scheme.

Exponential synchronization of Genesio–Tesi chaotic systems with partially known uncertainties and completely unknown dead-zone nonlinearity

Abstract This paper is concerned with the problem of synchronization controller design for Genesio–Tesi chaotic systems with plant uncertainties and dead-zone input. The upper bounds of plant uncertainties are partially known, while dead-zone nonlinearity is completely unknown. The prior knowledge on the parameters in the uncertainties and dead-zone is not required to be known in advance. A novel control law with adaptive methodology is proposed to compensate for input nonlinearity. An adaptive law with exponent function is designed to estimate the unknown lumped parameters. It is shown that complete synchronization between two identical Genesio–Tesi chaotic systems is achieved and the synchronization errors converge to zero exponentially. Numerical studies are provided to illustrate the effectiveness of the presented scheme.

Stability analysis of random systems with Markovian switching and its application

Abstract This paper aims to study a class of Markovian switching random systems with stochastic processes whose α-order moments ( α > 1 ) are finite. Compared with the existing results, the existence and uniqueness of solutions to random systems with Markovian switching is not given as a priori information but guaranteed under some general conditions. The corresponding criteria on noise-to-state stability and boundedness are presented by employing the Lyapunov method. Finally, based on the derived results, a design procedure of state-feedback tracking control is proposed, which is illustrated through two examples.