Improved stability criterion and its applications in delayed controller design for discrete-time systems

This paper is concerned with the problem of delay-dependent stability analysis for discrete-time systems with interval-like time-varying delays and the problem of stabilization for discrete-time linear systems via time-delayed controllers. The first problem is solved by applying a novel Lyapunov functional, and an improved delay-dependent stability criterion is obtained in terms of a linear matrix inequality. Based on this, a sufficient condition for the solvability of the second problem is presented. The reduced conservatism of the proposed stability result is shown through a numerical example, while the applicability of the time-delayed controller design method is demonstrated by an inverted pendulum system.     

Delay-dependent stability for discrete systems with large delay sequence based on switching techniques

This paper considers the exponential stability problem for a class of discrete time-varying delay systems with large delay sequences (LDSs). A new method based on a switching technique is presented to solve this problem. A switched delay system, in which one of the discrete subsystems may be unstable, is firstly employed to describe such a system, and then some new concepts about LDSs are introduced. Next, using a novel piecewise Lyapunov functional, explicit delay-dependent conditions are developed to show how long and how frequent the LDSs can be and still maintain the system exponentially stable. Without LDSs, the criterion obtained in this paper includes the established one as a special case. Two numerical examples are given to show the effectiveness of the proposed method.     

On loop phase margins of multivariable control systems

This paper has two contributions. One is introduction of loop phase margins for multivariable control systems, which extends the concept of phase margin in SISO systems to MIMO systems. The other one is development of an algorithm for computing the loop phase margins. The algorithm is composed of two steps. The first is to find the stabilizing ranges of loop time delay perturbations of the MIMO system using an LMI-based stability criterion derived here. The second is to convert these stabilizing ranges of loop time delays into the stabilizing ranges of loop phases. Two numerical examples are given to illustrate the effectiveness of the proposed approach.     

Relaxed delay-dependent exponential stability condition for a class of neural networks with polytopic uncertainties and distributed delays

The global robust exponential stability of a class of neural networks with polytopic uncertainties and distributed delays is investigated in this paper.Parameter-dependent Lypaunov-Krasovskii functionals and free-weighting matrices are employed to obtain sufficient condition that guarantee the robust global exponential stability of the equilibrium point of the considered neural networks.The derived sufficient condition is proposed in terms of a set of relaxed linear matrix inequalities (LMIs),which can be checked easily by recently developed algorithms solving LMIs.A numerical example is given to demonstrate the effectiveness of the proposed criteria.     

Delay-dependent stability of discrete-time interconnected systems

This paper studies the delay-dependent stability problem of discrete-time interconnected systems with timevarying delays. By using vector Lyapunov function approach and linear matrix inequalities (LMIs), new stability conditions are derived. These results proposed in this paper are all at subsystems level. After comparing with the existing results, it is shown that these conditions are less conservative. A numerical example is presented to demonstrate the effectiveness of the results.     

An improved approach to delay-dependent robust stabilization for uncertain singular time-delay systems

In this paper, delay-dependent stability analysis and robust stabilization for uncertain singular time-delay systems are addressed. By using Jensen integral inequality, an improved delay-dependent criterion of admissibility for singular time-delay systems is proposed in terms of linear matrix inequality (LMI). Our new proposed criterion is less conservative and the numerical complexity is smaller than the existing ones. Based on this criterion, a state feedback controller is designed to ensure that the uncertain singular time-delay system is admissible. Finally, three numerical examples are employed to illustrate the effectiveness of the proposed method.     

New results on robust exponential stability for discrete recurrent neural networks with time-varying delays

This paper is concerned with the problem of robust exponential stability analysis for uncertain discrete recurrent neural networks with time-varying delays. In terms of linear matrix inequality (LMI) approach, some novel stability conditions are proposed via a new Lyapunov function. Neither any model transformation nor free-weighting matrices are employed in our theoretical derivation. The established stability criteria significantly improve and simplify some existing stability conditions. Numerical examples are given to demonstrate the effectiveness of the proposed methods.     

Delay-dependent H-infinity control for continuous time-delay systems via state feedback

The delay-dependent H-infinity analysis and H-infinity control problems for continuous time-delay systems are studied. By introducing an equality with some free weighting matrices, an improved criterion of delay-dependent stability with H-infinity performance for such systems is presented, and a criterion of existence and some design methods of delay-dependent H-infinity controller for such systems are proposed in term of a set of matrix inequalities, which is solved efficiently by an iterative algorithm. Further, the corresponding results for the delay-dependent robust H-infinity analysis and robust H-infinity control problems for continuous time-delay uncertain systems are given. Finally, two numerical examples are given to illustrate the efficiency of the proposed method by comparing with the other existing results.     

Delay-dependent robust H-infinity control for discrete-time uncertain systems with time-varying state delays

1 Introduction The analysis and synthesis of dynamic control systems with time delays is a subject of great practical and theo- retical importance, and has received considerable attention for decades (see [1,2] and references therein). Stability cri- teria can be classified roughly into two categories: delay- independent and delay-dependent [3]. Delay-independent criteria contains no information on the delay size, which, as might be expected, is generally conservative, especially when the dela…     

Delay identification in time-delay systems using variable structure observers

In this paper we discuss delay estimation in time-delay systems. In the introduction section a short overview is given of some existing estimation techniques as well as identifiability studies. In the following sections we propose several algorithms for the delay identification based on variable structure observers.