Robust D-stability analysis for discrete uncertain systems with multiple time delays

Optimal D-stable control for discrete multiple time-delay systems with parametric uncertainties

In this paper, work concerning robust D-stability analysis is considered for discrete descriptor systems with structured uncertainties and multiple time delays. A genetic algorithm is used to make the stability test of the main result more efficient. A delay-dependent robust D-stability criterion is proposed to ensure that all poles of the discrete multiple time-delay descriptor systems subject to uncertainties are located within a disk contained in the unit circle. It will be seen that the system considered in this paper is more general and the proposed robust D-stability criterion is less conservative and easier to check than those presented in recent research. Moreover, a delay-dependent criterion is derived to guarantee that the system is regular, impulse-free, and D-stable. Since the boundary test occurs during the check of the criteria, a genetic algorithm is used to make it more precise. Finally, an example is introduced to illustrate our main results.

It is well known that the modeling issues in Dynamical systems in chemical processes, networked control systems and automation systems are very complex and model may contain subsystems with different delays. Because of the mathematical complexity, the robust control of these types of multiple time delay system is a challenging one. The problem becomes more difficult and complex when the system is having time delays in both the denominator and the numerator. In this paper a new method is proposed for approximating general multiple time delay continuous-time transfer function system with multiple time delays in both the denominator and the numerator to a single input/output delay. Both Single Input Single Output(SISO) and Multi Input Multi Output(MIMO) cases have been considered. In this proposed methodology, the Approximated Generalized Time Moments (AGTM)/ Approximated Generalized Markov Parameter (AGMP) methods are used to transform the multiple time delay system into a single input/output delay system. A Linear Matrix Inequality (LMI) approach is developed for synthesizing robust H∞ control of the approximated time delay system. The efficacy of the proposed method is shown through illustrative examples. It is evident from the simulation results that the approximated system is stable with the proposed LMI H∞ controller.

In this article, we study the controllability of finite-dimensional dynamical control systems modelled by semilinear impulsive ordinary differential equations with multiple constant time delays in the control function. Initially, we recall a necessary and sufficient condition for the controllability of the corresponding linear system without impulses, with multiple constant time delays in the control function in terms of a matrix rank condition. Then under some sufficient conditions, we show that the actual system is also controllable for certain classes of non-linearities and impulse functions. We employ Schauder fixed-point theorem and Banach contraction mapping principle to establish the results. Our obtained results are applicable for both autonomous and non-autonomous systems. An example is given to illustrate the theoretical results.

The problem of iterative learning control is considered for linear discrete-time systems with multiple time delays. In this paper, it is assumed that the initial condition for discrete time-delay systems is unknown at each iteration. For such a class of discrete time-delay systems, a method is presented whereby a class of P-type discrete iterative learning control schemes can be constructed. It is shown that under some given conditions, the constructed iterative learning controllers can guarantee the asymptotic convergence of the output error between the given desired output and the actual output through the iterative learning process. Finally, a numerical example is given to demonstrate the validity of the results.

Robust linear controller design of uncertain discrete systems with time-varying delay

Exponential stability criteria of uncertain systems with multiple time delays

<p style='text-indent:20px;'>This research paper deals with the investigation of global robust stability results for Cohen-Grossberg neural networks involving the multiple constant time delays. The activation functions in this neural network model are supposed to be in the set of non-decreasing slope-bounded nonlinear functions and the uncertainties in the constant network parameters are considered to have bounded upper norms. By employing a proper positive definite Lyapunov-type functional and using homeomorphism mapping theory, we propose some novel sets of novel conditions that assure both existence, uniqueness and global robust asymptotic stability of equilibrium points of this nonlinear Cohen-Grossberg-type neural network model involving the multiple time delays. The derived robustly stable conditions mainly rely on examining some proper relationships that are imposed on constant valued interconnection matrices of this delayed neural network. These stability conditions can be certainly verified by employing various simple and useful properties of real interval matrices. Some comparisons are made to address the key advantages of these novel criteria over previously reported corresponding results. An instructive example is also examined to observe novelty of these proposed criteria.</p>

Stability analysis for LTI systems with multiple time delays using the bounds of its imaginary spectra

WAMS (Wide-Area Measurement Systems) involve all kinds of communicating channels. Different channels have different time delays and randomicity of time-delay. So closed-loop power systems ought to be modeled as nonlinear dynamic systems with multiple time delays and varying time delays. A method is proposed in this paper to design a controller that can adapt to feedback signals with multiple time delays and varying time delays. The method is based on the topological characteristics of stable time-delay regions, the LMIs (Linear Matrix Inequalities) method, GA (Genetic Algorithm) and the balanced truncation model-reduced algorithm. Numerical results form a tow-area four-machine power system demonstrate that the controller derived from the above method can damp low-frequency oscillations in the system for the feedback signals with multiple time delays and varying time delays.

The robust stability analysis for discrete large-scale uncertain systems with multiple time delays is addressed in this paper. We establish a method for selecting properly a positive definite matrix Q to derive a very simple upper solution bound of the discrete algebraic Lyapunov equation (DALE). Then, using the Lyapunov equation approach method with this upper bound, several sufficient conditions are presented to guarantee the robust stability of the overall systems. Comparisons between the proposed results with a previous one are also given.

Novel results on projective synchronization of fractional-order neural networks with multiple time delays

The problem of guaranteed cost (GC) control using static-state feedback controllers for uncertain linear discrete time-delayed systems subjected to actuator saturation is studied in this paper. The stability analysis of closed-loop systems is carried out using a Lyapunov-Krasovskii functional. Conditions for the existence of state-feedback GC controllers are developed using a linear matrix inequality (LMI)-based criterion. The approach ensures a sufficient performance bound over all the acceptable parameter uncertainties. The scheme of the optimal GC controller problem is framed as a convex optimization problem with LMI constraints. The design of GC controllers for discrete-time systems subjected to actuator saturation without considering the effect of state-delay is also discussed. The effectiveness of the proposed approach is illustrated using suitable examples.

In this paper, a MIMO PI design procedure is proposed for linear time invariant (LTI) systems with multiple time delays. The controller tuning is established in two stages and guarantees performances for set‐point changes, disturbance variations, and parametric uncertainties. In the first stage, an iterative linear matrix inequality (ILMI) approach is extended to design PI controllers for systems with multiple time delays without performance guarantee, a priori. The second stage is devoted to improve the closed‐loop performances by minimizing sensitivity functions. Simulations results carried out on the unstable distillation column, the stable industrial scale polymerization (ISP) reactor, and the non‐minimum phase 4‐tank benchmark prove the efficiency of the proposed approach. A comparative analysis with the conventional internal model control (IMC) approach, a multiloop IMC‐PI approach, and a previous ILMI PID approach proves the superiority of the proposed approach compared to the related ones.

This paper investigates the robust stabilization of uncertain time-delayed systems via delta operator approach. By introducing model transportation, the linear delta operator system with time-varying delays is reformulated into an interconnected system for which the uncertainties can become easy to deal with. Based on a two-term approximation and scaled small gain theorem, a new delay-dependent sufficient condition of state feed-back stabilization for an uncertain delta operator time-delayed system is established by using a novel Lyapunov-Krasovskii functional. The condition obtained can unify some previously suggested relevant methods seen in literature for achieving asymptotic stabilization of both continuous and discrete systems into the delta operator framework. Numerical examples presented explicitly demonstrate the advantages and effectiveness of the proposed method.