Dependent Stability Conditions Research Articles

Integral Partitioning Approach to Stability Analysis and Stabilization of Distributed Time Delay Systems

AbstractIn this paper, the problems of delay-dependent stability analysis and stabilization are investigated for linear continuous-time systems with distributed delay. By introducing an integral partitioning technique, a new form of Lyapunov-Krasovskii functional (LKF) is constructed and improved distributed delay dependent stability conditions are established in terms of linear matrix inequalities (LMIs). Based on the criteria, a design algorithm for a state feedback controller is proposed. The results developed in this paper are less conservative than existing ones in the literature, which is illustrated by several examples.

Delay Dependent Robust Exponential Stability Criterion for Perturbed and Uncertain Neutral Systems with Time Varying Delays

This paper deals with the issue of robust exponential stability of uncertain neutral system with time varying delay and nonlinear perturbations. Using Lyapunov-Krasovskii functional, new sufficient delay dependent stability conditions have been derived in terms of Linear Matrix Inequalities LMIs solved using efficient convex optimization algorithms. Neither model transformation, nor estimating techniques for cross terms, nor free weighting matrices are involved in this work. Numerical examples are considered to show the efficiency of the proposed stability approach.

Robustness of a discrete-time predictor-based controller for time-varying measurement delay

A predictor-based controller for time-varying delay systems is presented in this paper and its robustness properties for different uncertainties are analyzed. First, a time-varying delay dependent stability condition is expressed in terms of LMIs. Then, uncertainties in the knowledge of all plant-model parameters are considered and the resulting closed-loop system is shown to be robust with respect to these uncertainties. A significant improvement with respect to the same control strategy without predictor is achieved. The scheme is applicable to open-loop unstable plants and it has been tested in a real-time application to control the roll angle of a quad-rotor helicopter prototype. The experimental results show good performance and robustness of the proposed scheme even in the presence of long delay uncertainties.

Improved exponential stability for time-varying systems with nonlinear delayed perturbations

In this paper, a new sufficient delay dependent exponential stability condition for a class of linear time-varying systems with nonlinear delayed perturbations is derived by using an improved Lyapunov–Krasovskii functional. The proposed exponential stability conditions are formulated in terms of the solution of Lyapunov differential equations. The approach allows for computation of the bounds that characterize the exponential stability rate of convergence of the solution. Compared with existing results, our conditions are shown to be less conservative. Numerical examples are given to illustrate the effectiveness of the obtained conditions.

Computational Effective Stability Conditions for Time-delay Fuzzy Systems

This paper investigates the system stability of the time-delay fuzzy-model-based control systems based on delay-independent and -dependent approaches. LMI-based delay-independent and -dependent stability conditions are derived to guarantee the system stability using Lyapunov-based technique. It can be seen that some existing stability analysis approaches require high computational demand to solve the solution due to the large number of stability conditions. Consequently, feasible solution may not be obtained with the use of numerical methods due to the limitation of the computer system especially for complicated fuzzy systems with a large number of rules. In this paper, under a particular system formulation, the number of stability conditions can be reduced to alleviate the computational demand on searching for the solution. Furthermore, the stability conditions offer a larger upper bound of time delay compared with some existing approaches. LMI-based performance conditions are also derived to guarantee the system performance. Simulation examples are given to illustrate the merits of the proposed approaches.

Stabilization of remote control systems with unknown time varying delays by LMI techniques

In this paper, the stabilization of one class of remote control systems with unknown time varying delays is analysed and discussed using LMI techniques. A discrete time state space model under a static control law for remote control systems is first introduced based on some assumptions on the uncertain term. The time delay is unknown, time varying, and can be decomposed into two parts: one fixed part which is unknown and is an integer multiple of the sampling time; the other part which is randomly varying but bounded by one sampling time. Static controller designs based on delay dependent stability conditions are presented. This system is then extended to a more general case when the randomly varying part of the time delay is not limited to one sampling time. The derivative of the time delay is not limited to be bounded. Hence, the contributions are as follow: (i) for a given controller, we can use these stability criteria to test stability of the resulted system; (ii) we can design a remote controller to stabilize an unstable system. Finally, simulation examples are presented to show the effectiveness of the proposed method and to demonstrate remote stabilization of open loop unstable systems.

Vertex Stability Results for a Diamond-Type Family of Quasipolynomials

A class of diamond polynomial families is introduced, for which vertex type stability results hold. Such families are in turn the tool for deriving quasipolynomial families for which both delay dependent and delay independent stability conditions are given.

Polytopic families of quasi-polynomials: vertex-type stability conditions

Quasi-polynomial families generated by multivariate interval polynomials are considered. It is shown that for these families both delay independent and delay dependent vertex-type stability conditions hold.

Delay Dependent Stability Conditions for Linear Time Varying Systems

A special transformation of time delay systems is studied. Delay dependent stability conditions for a transformed linear time varying system with delay are compared with that of the original one. Additional stability conditions inposed by the transformation are derived.

Stability Condition of State-Delayed Systems Based on Stability-Guaranteed Discretization

This paper proposes a new delay dependent stability condition for state-delayed systems. This stability condition is based on the discretization of an infinite dimensional kernel of state-delayed systems and provides a check condition when the stability of the discretized system implies state-delayed systems. This check condition is derived using a lifting technique and is given in the form of discrete system H/sub /spl infin// norm test. The stability condition is shown to converge to the exact stability condition when the order of discretization approaches infinity.

On the modulational instability of hydromagnetic waves parallel to the magnetic field

The stability of circularly polarized waves of finite amplitude propagating parallel to the magnetic field is studied. A set of equations for slowly varying waves of arbitrary amplitude is obtained. A discussion of the stability of the waces is based on this set of equations. Earlier results are confirmed; in addition we find that finite amplitude always promotes stability. An amplitude dependent stability condition for long waves, previously obtained by the author, is confirmed.