Hanyong Shao

New Stability Criteria for Linear Discrete-Time Systems With Interval-Like Time-Varying Delays

This technical note is concerned with stability of linear discrete-time systems with interval-like time-varying delays. Two new stability criteria are derived by constructing a new Lyapunov functional and utilizing two novel techniques for estimating the forward difference of the Lyapunov functional. The relationship between these stability criteria and some existing ones is established. Through the relationship, it is clear that these stability criteria are less conservative than some existing ones, which is confirmed by a numerical example.

Delay-Dependent Stability for Recurrent Neural Networks With Time-Varying Delays

This brief is concerned with the stability for static neural networks with time-varying delays. Delay-independent conditions are proposed to ensure the asymptotic stability of the neural network. The delay-independent conditions are less conservative than existing ones. To further reduce the conservatism, delay-dependent conditions are also derived, which can be applied to fast time-varying delays. Expressed in linear matrix inequalities, both delay-independent and delay-dependent stability conditions can be checked using the recently developed algorithms. Examples are provided to illustrate the effectiveness and the reduced conservatism of the proposed result.

New Delay-Dependent Stability Criteria for Neural Networks With Two Additive Time-Varying Delay Components

This brief is concerned with delay-dependent stability for neural networks with two additive time-varying delay components. By constructing a new Lyapunov functional and using a convex polyhedron method to estimate the derivative of the Lyapunov functional, some new delay-dependent stability criteria are derived. These stability criteria are less conservative than some existing ones. An example is given to demonstrate the less conservatism of the stability results.

Less conservative delay-dependent stability criteria for linear systems with interval time-varying delays

This article provides new delay-dependent stability criteria for linear systems with interval time-varying delays. With a new Lyapunov–Krasovskii functional constructed, a tighter upper bound of its derivative is estimated. The resulting criterion has an advantage over some existing ones in the literature due to the fact that it involves fewer matrix variables and is less conservative, which is established theoretically. Two numerical examples are given to demonstrate the reduced conservatism of the proposed results.

On stabilization for systems with two additive time-varying input delays arising from networked control systems

Abstract This paper is concerned with the stability and stabilization for systems with two additive time-varying input delays arising from networked control systems. A new Lyapunov functional is constructed and a tighter upper bound of the derivative of the Lyapunov functional is derived by applying a convex polyhedron method. The resulting stability criteria are of fewer matrix variables and less conservative than some existing ones. Based on the stability criteria, a state feedback controller is designed such that the closed-loop system is asymptotically stable. Numerical examples are given to show the less conservatism of the stability criteria and the effectiveness of the designed method.

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.

A new approach to sampling-dependent stability for sampled-data systems under aperiodic samplings

This paper is concerned with a new Lyapunov functional approach to sampling-dependent stability for sampled-data systems under aperiodic samplings. A new Lyapunov functional is constructed by introducing the integral of the state. The improved Jensen inequality reported recently is used to estimate the derivative of the Lyapunov functional. Based on Lyapunov stability theory, a new sampling-dependent stability result is obtained for sampled-data systems under aperiodic samplings. Then, this stability result is extended to sampled-data systems with polytopic uncertainties under aperiodic samplings. At last, simulations show that the proposed results have less conservatism than some existing ones.

A Lyapunov-like functional approach to stability for impulsive systems with polytopic uncertainties

Abstract This paper is concerned with a Lyapunov-like functional approach to stability for impulsive systems with polytopic uncertainties. At first, a Lyapunov-like functional approach is established to investigate the stability for impulsive systems, with the Lyapunov-like functional dependent on time explicitly, discontinuous, and not imposed to be definite positive. A specific Lyapunov-like functional is created by introducing the integral of the system state and the cross terms among this integral and the impulsive state. To estimate the derivative of the functional, a new inequality is proposed, and an integral equation of the impulsive system is employed. By the Lyapunov-like functional theory, a new asymptotical stability result is obtained for impulsive systems without uncertainties. Then, the stability result is further extended to impulsive systems with polytopic uncertainties. At last, some numerical examples are given to illustrate that the proposed stability results have less conservatism than some existing ones.

Novel stability criteria for sampled-data systems with variable sampling periods

This paper is concerned with a novel Lyapunovlike functional approach to the stability of sampled-data systems with variable sampling periods. The Lyapunov-like functional has four striking characters compared to usual ones. First, it is time-dependent. Second, it may be discontinuous. Third, not every term of it is required to be positive definite. Fourth, the Lyapunov functional includes not only the state and the sampled state but also the integral of the state. By using a recently reported inequality to estimate the derivative of this Lyapunov functional, a sampled-interval-dependent stability criterion with reduced conservatism is obtained. The stability criterion is further extended to sampled-data systems with polytopic uncertainties. Finally, three examples are given to illustrate the reduced conservatism of the stability criteria.

Sampling-interval-dependent stability for sampled-data systems with variable sampling

This paper aims at sampling-interval-dependent stability of sampled-data systems with variable sampling. A new Lyapunov-like functional is first constructed to derive sampling-interval-dependent stability results. The Lyapunov-like functional has three features. First, it depends on time explicitly. Second, it may be discontinuous at the sampling instants. Third, it is not required to be positive definite within a sampling interval. Moreover, the new Lyapunov-like functional can employ the information of both ends of the sampling interval. By proposing a new lemma to estimate the derivative for this Lyapunov-like functional, a less conservative sampling-interval-dependent stability criterion is derived. When the sampled-data system involves polytopic uncertainties, a robust sampling-interval-dependent stability criterion is also obtained. Finally, two examples are listed to illustrate the reduced conservatism of the stability criteria.