Robust L2 - L∞ filtering for a class of dynamical systems with nonhomogeneous Markov jump process

This paper investigates the problem of robust L2 - L∞ filtering for a class of dynamical systems with nonhomogeneous Markov jump process. The time-varying transition probabilities which evolve as a nonhomogeneous jump process are described by a polytope, and parameter-dependent and mode-dependent Lyapunov function is constructed for such system, and then a robust L2 -L8 filter is designed which guarantees that the resulting error dynamic system is robustly stochasticallystable and satisfies a prescribed L2 - L∞ performance index. A numerical example is given to illustrate the effectiveness of the developed techniques

Quantized passive filtering for switched delayed neural networks

The issue of quantized passive filtering for switched delayed neural networks with noise interference is studied in this paper. Both arbitrary and semi-Markov switching rules are taken into account. By choosing Lyapunov functionals and applying several inequality techniques, sufficient conditions are proposed to ensure the filter error system to be not only exponentially stable, but also exponentially passive from the noise interference to the output error. The gain matrix for the proposed quantized passive filter is able to be determined through the feasible solution of linear matrix inequalities, which are computationally tractable with the help of some popular convex optimization tools. Finally, two numerical examples are given to illustrate the usefulness of the quantized passive filter design methods

Multiobjective nonfragile fuzzy control for nonlinear stochastic financial systems with mixed time delays

In this study, a multiobjective nonfragile control is proposed for a class of stochastic Takagi and Sugeno (T–S) fuzzy systems with mixed time delays to guarantee the optimal H2 and H∞ performance simultaneously. Firstly, based on the T–S fuzzy model, two form of nonfragile state feedback controllers are designed to stabilize the T–S fuzzy system, that is to say, nonfragile state feedback controllers minimize the H2 and H∞ performance simultaneously. Then, by applying T–S fuzzy approach, the multiobjective H2/H∞ nonfragile fuzzy control problem is transformed into linear matrix inequality (LMI)-constrained multiobjective problem (MOP). In addition, we efficiently solve Pareto optimal solutions for the MOP by employing LMI-based multiobjective evolution algorithm (MOEA). Finally, the validity of this approach is illustrated by a realistic design example

Fault Detection Filter for Discrete-Time Markov Jump Lur’e Systems

We present the design of H_inf Fault Detection Filter (FDF) for Discrete-time Markov Jump Lur'e Systems with bounded sector condition based on the use of Linear Matrix Inequality (LMI). A numerical example is presented to illustrate the effectiveness of the proposed approach

Event-triggered proportional-derivative control for nonlinear network systems with a novel event-triggering scheme: Differential of triggered state consideration

This article proposes event-triggered proportional-derivative control for a class of nonlinear network control systems. For derivative action of the proposed proportional-derivative control, a novel event-triggering scheme is devised together with the control that considers a differential of a triggered state. The class of the nonlinear network systems is represented as a Lur'e system to consider various nonlinear cases. Time varying transmission delay is considered which can be defined by lower and upper delay bounds. The proposed proportional-derivative control is designed by Lyapunov-Krasovskii stability analysis, and the design condition is presented by linear matrix inequalities. The proposed event-triggered proportional-derivative control and event-triggering condition are verified with numerical simulation. ? 2017 The Author(s).111Ysciescopu

Dissipative Analysis and Synthesis of Control for TS Fuzzy Markovian Jump Neutral Systems

This paper is focused on stochastic stability and strictly dissipative control design for a class of Takagi-Sugeno (TS) fuzzy neutral time delayed control systems with Markovian jumps. The main aim of this paper is to design a strictly dissipative controller such that the closed-loop TS fuzzy control system is stochastically stable, and also the disturbance rejection attenuation is obtained to a given level by means of the H∞ performance index. Intensive analysis is carried out to obtain sufficient conditions for the existence of desired dissipative controller which ensures both the stochastic stability and the strictly dissipative performance. The main advantage of the proposed technique is that it is possible to obtain the dissipative controller with less control effort and also, as special cases, robust H∞ control with the prescribed H∞ performance under given constraints and passivity control can be obtained for the considered systems. Also, the existence condition of the fuzzy dissipative controller can be obtained in terms of linear matrix inequalities. Finally, a practical example based on truck-trailer model is provided to demonstrate the effectiveness and feasibility of the proposed design technique

H∞ model reduction for discrete-time Markovian jump systems with deficient mode information

This paper investigates the problem of H∞ model reduction for a class of discrete-time Markovian jump linear systems (MJLSs) with deficient mode information, which simultaneously involves the exactly known, partially unknown, and uncertain transition probabilities. By fully utilizing the properties of the transition probability matrices, together with the convexification of uncertain domains, a new H∞ performance analysis criterion for the underlying MJLSs is first derived, and then two approaches, namely, the convex linearisation approach and iterative approach, for the H∞ model reduction synthesis are proposed. Finally, a simulation example is provided to illustrate the effectiveness of the proposed design methods

Static anti-windup compensator design for locally Lipschitz systems under input and output delays

This paper proposes a static anti-windup compensator (AWC) design methodology for the locally Lipschitz nonlinear systems, containing time-varying interval delays in input and output of the system in the presence of actuator saturation. Static AWC design is proposed for the systems by considering a delay-range-dependent methodology to consider less conservative delay bounds. The approach has been developed by utilizing an improved Lyapunov-Krasovskii functional, locally Lipschitz nonlinearity property, delay-interval, delay derivative upper bound, local sector condition, L2 gain reduction from exogenous input to exogenous output, improved Wirtinger inequality, additive time-varying delays, and convex optimization algorithms to obtain convex conditions for AWC gain calculations. In contrast to the existing results, the present work considers both input and output delays for the AWC design (along with their combined additive effect) and deals with a more generic locally Lipschitz class of nonlinear systems. The effectiveness of the proposed methodology is demonstrated via simulations for a nonlinear DC servo motor system, possessing multiple time-delays, dynamic nonlinearity and actuator constraints

Nonlinear Systems

Open Mathematics is a challenging notion for theoretical modeling, technical analysis, and numerical simulation in physics and mathematics, as well as in many other fields, as highly correlated nonlinear phenomena, evolving over a large range of time scales and length scales, control the underlying systems and processes in their spatiotemporal evolution. Indeed, available data, be they physical, biological, or financial, and technologically complex systems and stochastic systems, such as mechanical or electronic devices, can be managed from the same conceptual approach, both analytically and through computer simulation, using effective nonlinear dynamics methods. The aim of this Special Issue is to highlight papers that show the dynamics, control, optimization and applications of nonlinear systems. This has recently become an increasingly popular subject, with impressive growth concerning applications in engineering, economics, biology, and medicine, and can be considered a veritable contribution to the literature. Original papers relating to the objective presented above are especially welcome subjects. Potential topics include, but are not limited to: Stability analysis of discrete and continuous dynamical systems; Nonlinear dynamics in biological complex systems; Stability and stabilization of stochastic systems; Mathematical models in statistics and probability; Synchronization of oscillators and chaotic systems; Optimization methods of complex systems; Reliability modeling and system optimization; Computation and control over networked systems