In this paper, we introduce the notion of h-stability for set-valued differential equations. Necessary and sufficient conditions are established by using Lyapunov theory. Then, based on the obtained results, we study the ℎ-stability of perturbed and cascaded systems. Finally, an example illustrates the proposed theorems

Disturbance rejection performance optimization with constraints on robustness for a multivariable process is commonly encountered in industrial control applications. This paper presents the tuning of a multi-loop Proportional Integral (PI) controller method to enhance the performance of load disturbance rejection using evolutionary optimization. The proposed design methodology is formulated to minimize the load disturbance rejection response and the input control energy under the constraints of robust stability. The minimum singular value of multiplicative uncertainty is considered a multi-loop system robust stability indicator. Optimization is performed to achieve the same, or higher level than the most-explored Direct Synthesis (DS) based multi-loop PI controller, which is derived from a conventional criterion. Simulation analysis clearly proved that the proposed multi-loop PI controller tuning method gives better disturbance rejection, and either, the same or a higher level of robust stability when compared to the DS-based multi-loop PI controller.

A boundary value problem for a non-linear difference equation of order three is considered. We show that this equation can be interpreted as the equation satisfied by the value function in a stochastic optimal control problem. We thus obtain an expression for the solution of the non-linear difference equation that can be used to find an explicit solution to this equation. An example is presented.

The current task explores automatic generation control knowledge under old-style circumstances for a triple-arena scheme. Sources in area-1 are thermal-solar thermal (ST); thermalgeothermal power plant (GPP) in area-2 and thermal-hydro in area-3. An original endeavour has been set out to execute a new performance index named hybrid peak area integral squared error (HPA-ISE) and two-stage controller with amalgamation of proportional-integral and fractional order proportional-derivative, hence named as PI(FOPD). The performance of PI(FOPD) has been compared with varied controllers like proportional-integral (PI), proportional-integralderivative (PID). Various investigation express excellency of PI(FOPD) controller over other controller from outlook regarding lessened level of peak anomalies and time duration for settling. Thus, PI(FOPD) controller’s excellent performance is stated when comparison is undergone for a three-area basic thermal system. The above said controller’s gains and related parameters are developed by the aid of Artificial Rabbit Optimization (ARO). Also, studies with HPA-ISE enhances system dynamics over ISE. Moreover, a study on various area capacity ratios (ACR) suggests that high ACR shows better dynamics. The basic thermal system is united with renewable sources ST in area-1 also GPP in area-2. Also, hydro unit is installed in area-3. The performance of this new combination of system is compared with the basic thermal system using PI(FOPD) controller. It is detected that dynamic presentation of new system is improved. Action in existence of redox flow battery is also examined which provides with noteworthy outcome. PI(FOPD) parameters values at nominal condition are appropriate for higher value of disturbance without need for optimization.

In this work, a new 3-D modified WINDMI chaotic jerk system with exponential and sinusoidal nonlinearities is presented and its dynamical behaviours and properties are investigated. Firstly, some properties of the system are studied such as equilibrium points and their stability, Lyapunov exponents and Kaplan-Yorke dimension. Also, we study the new jerk system dynamics using numerical simulations and analyses, including phase portraits, Lyapunouv exponent spectrum, bifurcation diagram and Poincaré map, 0-1 test. Next, we exhibit that the new 3-D chaotic modified WINDMI jerk system has multistability with coexisting chaotic attractors. Moreover, we design an electronic circuit using MultiSim 14.1 for real implementation of the modified WINDMI chaotic jerk system. Finally, we design an active synchronization scheme for the complete synchronization of the modified WINDMI chaotic jerk systems via backstepping control.

This article concerns the use of an integrated RFID system with a mobile robot for the navigation and mapping of closed spaces. The architecture of a prototype mobile robot equipped with a set of RFID readers that performs the mapping functions is described. Laboratory tests of the robot have been carried out using a test stand equipped with a grid of appropriately programmed RFID transponders. A simulation model of the effectiveness of transponder reading by the robot has been prepared. The conclusions from measurements and tests are discussed, and methods for improving the solution are proposed.

This paper presents equivalent impedance and operator admittance systems for fractional order elements. Presented models of fractional order elements of the type: s ^α L _α and 1/s ^α C _α, (0 α 1) were obtained using the Laplace transform based on the expansion of the factor sign to an infinite fraction with varying degrees of accuracy – the continued fraction expansion method (CFE). Then circuit synthesis methods were applied. As a result, equivalent circuit diagrams of fractional order elements were obtained. The obtained equivalent schemes consist both of classical RLC elements, as well as active elements built based on operational amplifiers. Numerical experiments were conducted for the constructed models, presenting responses to selected input signals.

The asymptotic stability of the convex linear combination of continuous-time and discretetime linear systems is considered. Using the Gershgorin theorem it is shown that the convex linear combination of the linear asymptotically stable continuous-time and discretetime linear systems is also asymptotically stable. It is shown that the above thesis is also valid (even simpler) for positive linear systems.