Robust H∞ control for uncertain discrete-time state-delayed linear systems with markovian jumping parameters

Markovian jumping systems have arisen naturally in the mathematical modeling of phenomena spanning disciplines in the social sciences, natural sciences, and engineering. This kind of stochastic dynamical systems can be employed to model the dynamics when parameters are subject to random abrupt changes due to sudden environment changes, subsystem switching, system noises, executor faults, and so forth. Much attention has been given to modeling, optimization, and real applications of such stochastic dynamical systems in the literature in recent years. As the advanced control and optimization will provide a basis for the design and application of such stochastic systems, these advanced techniques would result in substantial and sustainable benefits. The accepted papers in this special issue include stochastic stability, stabilization, stochastic control optimization, system modeling and identification methods, predictive control, signal processing, robust filtering, multiagent systems, networked control systems, time-delayed systems, neural networks, the Takagi-Sugeno fuzzy systems, simulated annealing, and fault detection methods.

This paper considers a subclass of hybrid systems, which is the discrete-time linear switching systems whose changes in the dynamics are determined by exogenous, uncontrollable events, and resets are present. In the presence of uncertain parameter and non-symmetrical constrained control, based on the results of nominal linear switching systems, a necessary and sufficient condition to test the robustness of a state feedback controller is given. The candidate state feedback controller for this test is that stabilizing nominal discrete-time linear switching systems. Also, the method in this paper can be extended to the case which has state constraints. At last, a numerical example is presented to illustrate the technique.

Exponential stability criteria of uncertain systems with multiple time delays

In this paper, a combination of integral sliding mode and composite nonlinear feedback method is proposed for fast and accurate robust tracking and model following of uncertain multiple-input multiple-output linear systems with multiple time-delays and external disturbances. The composite nonlinear feedback technique allows following the reference trajectory within a given accuracy and the invariance property of the integral sliding mode method rejects the disturbances and preserves the stability of the closed-loop system. By using the Lyapunov–Krasovskii functional, the conditions for asymptotic stabilization are obtained in the form of linear matrix inequalities. To improve the tracking performance for different reference amplitudes, a new nonlinear function is included in the control law and is optimally tuned using a modified random search algorithm. The selection of sliding surface and the existence of the sliding mode are two significant issues, which have been addressed. This scheme not only guarantees robustness against time-delays and uncertainties, but also avoids chattering phenomenon and reaching phase. Finally, the simulations are provided to verify the theoretical results. The results show that the proposed method leads to great improvement on the tracking error and the control effort compared to the available methods.

This paper studies the design of uncertain linear discrete-time Networked Control Systems over imperfect communication channels with time-varying data loss. This leakage is modeled as stochastic parameter and norm-bounded uncertainties. In addition, this paper defines the necessary conditions for the design of the dynamic output feedback controller; subsequently, an iterative LMI approach is specified to compute the controller state parameters. The simulation results show that the designed controller improves the H∞ disturbance attenuation performance of the concerned uncertain system.

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.

This paper addresses the problem of robust /spl Hscr//sub /spl infin// filtering for linear discrete-time systems subject to parameter uncertainties in the system state-space model and with multiple time delays in the state variables. The uncertain parameters are supposed to belong to a given convex bounded polyhedral domain. A methodology is developed to design a stable linear filter that assures asymptotic stability and a prescribed /spl Hscr//sub /spl infin// performance for the filtering error, irrespective of the uncertainty and the time delays. The proposed design is given in terms of linear matrix inequalities, which has the advantage in that it can be implemented numerically very efficiently.

This paper deals with the robust stabilization problem of uncertain discrete-time saturating control systems with multiple time-delays. Some sufficient criteria for these systems are proposed. The state feedback controller is designed to ensure certain performance robustness. The results contain those of Chou (1991) as a special case.

<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>

Robust H ∞ controller design for linear uncertain systems with delayed state and control

This paper investigates the problem of robust control for a class of systems with both Markovian jumping parameters and parametric uncertainty. The jumping parameters considered here form a continuous-time discrete-state homogeneous Markov process, and the parameter uncertainty appearing in the state equation is real, time-dependent, and normbounded. A method is proposed for the design of robust state-feedback controllers. Both the cases of finite and infinite horizon are addressed. We show that the problem of robust control for linear systems with Markovian jumping parameters can be solved in terms of the solutions to a set of either coupled Riccati differential equations, or algebraic Riccati equations.

The problem of assigning all poles of a closed-loop system in a specified disk by dynamic output feedback is considered for discrete systems with multiple non-commensurate time delays. This kind of pole assignment problem is called D-pole placement, and its relation to robustness properties is discussed. Thus, the robust D-pole placement is subsequently proposed and a robust criterion is derived to ensure D-stability of the discrete multiple time-delay systems subject to parametric uncertainties. Furthermore, with this robust criterion, the bounds can also be estimated for allowable parametric uncertainties that guarantee all the poles of the discrete uncertain multiple time-delay systems to remain inside the specified disk. Finally, an example is given to illustrate obtained results. >

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.

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

This article is concerned with robust stability of uncertain discrete-time linear systems. The matrix defining the linear system (system matrix) is assumed to depend affinely on a set of time-invariant unknown parameters lying on a known polytope. Robust stability is investigated by checking whether a certain integer power κ of the uncertain system matrix has spectral norm less than one. This peculiar stability test is shown to be equivalent to the positivity analysis of a homogeneous symmetric matrix polynomial with precisely known coefficients and degree indexed by κ. A unique feature is that no extra variables need to be added to the problems being solved. Numerical experiments reveal that the value of κ needed to test robust stability is mostly independent of the system dimension but grows sharply as the eigenvalues of the uncertain system approach the unit circle. By identifying the proposed stability test with a particular choice of a parameter-dependent Lyapunov function, extra variables can be introduced, yielding linear matrix inequalities optimisation problems of improved convergence.