This paper investigates the novel sliding mode control design with state derivative output feedback in nontraditional reciprocal state space (RSS) form. The concepts and the need of RSS form are comprehensively reviewed and explained. Novel switching function and approaching condition based on the derivative of sliding surface are introduced. In addition, a sufficient condition for finding the upper bound of system uncertainty to guarantee the stability in sliding surface is developed for robustness analysis. A compact sliding mode controller utilizing only state derivative related output feedback is proposed for systems with system uncertainty, matched input uncertainty, and matched external disturbance. Simulation results for a circuit system successfully verify the validities of the proposed algorithms. Our derivation is basically parallel to that for systems in standard state space form. Therefore, those who understand the concepts of sliding mode control can easily apply our method to handle more control problems without being involved in complex mathematics.

This paper investigates the consensus problem for second-order leader-follower nonlinear multiagent systems with general network topologies. A pinning control algorithm is proposed, where it includes time-varying delay information. By using the information of delay-partition and delay-distribution and constructing an appropriate Lyapunov-Krasovskii functional, the consensus criteria are derived to achieve leader-follower consensus for multiagent systems, which are in the form of linear inequalities that can be solved by employing the semidefinite programme method. Moreover, this paper addresses what kind of agents and how many agents should be pinned. Two numerical examples are presented to further demonstrate the effectiveness of the proposed approach.

The equivalence of two conditions, condition (3) and condition (4) stated in Problem Statement section, regarding the existence of stabilizing switching laws between two unstable linear systems first appeared in (Feron 1996). Although Feron never published this result, it has been referenced in almost every survey on switched systems; see, for example, (Liberzon and Morse 1999). This paper proposes another way to prove the equivalence of two conditions regarding the existence of stabilizing switching laws between two unstable linear systems. One is effective for theoretical derivation, while the other is implementable, and a class of stabilizing switching laws have been explicitly constructed by Wicks et al. (1994). With the help of the equivalent relation, a condition for the existence of controllers and stabilizing switching laws between two unstabilizable linear control systems is then proposed. Then, the study is further extended to the issue concerning the construction of quadratically stabilizing switching laws among $N$ unstable linear systems and $N$ unstabilizable linear control systems. The obtained results are employed to study the existence of control laws and quadratically stabilizing switching laws within a class of unstabilizable linear control systems. The numerical examples are illustrated and simulated to show the feasibility and effectiveness of the proposed methods.

The Filippov ratio-dependent prey-predator model with economic threshold is proposed and studied. In particular, the sliding mode domain, sliding mode dynamics, and the existence of four types of equilibria and tangent points are investigated firstly. Further, the stability of pseudoequilibrium is addressed by using theoretical and numerical methods, and also the local sliding bifurcations including regular/virtual equilibrium bifurcations and boundary node bifurcations are studied. Finally, some global sliding bifurcations are addressed numerically. The globally stable touching cycle indicates that the density of pest population can be successfully maintained below the economic threshold level by designing suitable threshold policy strategies.

This paper proposes a spatial cooperative diversity and decision-making technique to enhance signal detection and indoor mobile robot positioning performance of a global positioning satellite system (GNSS) receiver. Though the adaptive antenna array technique in early research could effectively promote antijamming freedom, overcome time-varying system, and mitigate narrowband and wideband interferences, factors such as the decrease of signal magnitude caused by obstacles (especially in the indoor environment), multipath, and blanking effect caused by the change in antenna direction with the motion of mobile robot can degrade the detection and interference mitigation performance of GNSS receivers. This paper aims to develop a dynamic cooperative scheme to proceed with the switch, selection, combination, and optimization among antennas. In addition, a signal processing experimental platform is also established to receive actually indoor GNSS signals for verification. The proposed scheme is capable of effectively promoting the postcorrelation signal-to-noise ratio (SNR) capability of a GNSS receiver under the indoor environment.

This paper is focused on the study of the important property of the asymptotic hyperstability of a class of continuous-time dynamic systems. The presence of a parallel connection of a strictly stable subsystem to an asymptotically hyperstable one in the feed-forward loop is allowed while it has also admitted the generation of a finite or infinite number of impulsive control actions which can be combined with a general form of nonimpulsive controls. The asymptotic hyperstability property is guaranteed under a set of sufficiency-type conditions for the impulsive controls.

This paper deals with the finite-time stabilization problem for discrete-time Markov jump nonlinear systems with time delays and norm-bounded exogenous disturbance. The nonlinearities in different jump modes are parameterized by neural networks. Subsequently, a linear difference inclusion state space representation for a class of neural networks is established. Based on this, sufficient conditions are derived in terms of linear matrix inequalities to guarantee stochastic finite-time boundedness and stochastic finite-time stabilization of the closed-loop system. A numerical example is illustrated to verify the efficiency of the proposed technique.

We present an advanced design methodology for pulse-width-modulated (PWM) DC-AC signal generation. Using design methods based on the Walsh transform, AC sinusoidal signals can be approximated by suitable PWM signals. For different AC amplitudes, the switching instants of the PWM signals can be efficiently computed by using appropriate systems of explicit linear equations. However, the equation systems provided by conventional implementations of this approach are typically only valid for a restricted interval of AC amplitudes and, in general, a supervised implementation of several equation systems is necessary to cover the full AC amplitude range. Additionally, obtaining suitable equation systems for designs with a large number of switching instants requires solving a complex optimization problem. In defining the constitutive pulses of a PWM signal, a suitable partition of the time interval is used as a reference system. In the new methodology, pulses are chosen to be symmetric with respect to the partition points, and the switching times are specified by means of switching ratios with respect to the endpoint subintervals. This approach leads to particularly simple Walsh series representations, introduces a remarkable computational simplification, and achieves excellent results in reducing the harmonic distortion.

This paper studies the stabilization of second-order switched homogeneous systems. We present results that solve the problem of stabilizing a switched homogeneous system; that is, we establish necessary and sufficient conditions under which the stabilization is assured. Moreover, given an initial condition, our method determines if there exists a switching law under which the solution converges to the origin and, if there exists this switching law, how it is constructed. Finally, two numerical examples are presented in order to illustrate the results.

We investigate the problem of coordinated formation control for multiple surface vessels in the presence of unknown external disturbances. In order to realize the leaderless coordinated formation and achieve the robustness against unknown external disturbances, a new robust coordinated formation control algorithm based on backstepping sliding mode control is proposed. The proposed coordinated control algorithm is achieved by defining a new switched function using the combination of position tracking error and cross-coupling error. Particularly, the cross-coupling error is defined using velocity tracking error and velocity synchronization error so as to be applicable for sliding mode controller design. Furthermore, the adaptive control law is proposed to estimate unknown disturbances for each vessel. The globally asymptotically stability is proved using the Lyapunov direct method. Finally, the effectiveness of the proposed coordinated formation control algorithm is demonstrated by corresponding simulations.

The paper presents a novel feedback linearization controller of nonlinear multiinput multioutput time-delay large-scale systems to obtain both the tracking and almost disturbance decoupling (ADD) performances. The significant contribution of this paper is to build up a control law such that the overall closed-loop system is stable for given initial condition and bounded tracking trajectory with the input-to-state-stability characteristic and almost disturbance decoupling performance. We have simulated the two-inverted-pendulum system coupled by a spring for networked control systems which has been used as a test bed for the study of decentralized control of large-scale systems.

This paper focuses on the time delay estimation of the system described in the form of discrete-time state equation with multiple input delays. To estimate the input delays, a new evolutionary computation called the artificial bee colony (ABC) algorithm is utilized. This algorithm is originally motivated from the social behaviors of honeybee organization, and it has been proven to be a powerful means for solving the optimized problem. Based on the proposed algorithm, the unknown system input delays can be further solved by minimizing a quadratic cost function of the system. Two illustrative examples are provided to verify the potential of the presented method in the time delay estimation. Some simulations containing different initial condition examinations and appearance of noises are further given. Numerical results show that the proposed method can do well in the multiple inputs delay estimation of discrete-time state equations.

Building energy consumption monitoring and management system have been developed widely in China in order to gain the real-time data of energy consumption in buildings for analyzing it in the next state work. This paper describes a low-cost and small-sized collector based on the STM32 microcontroller, which can be placed in a building easily to implement the work of data acquisition, storage, and transmission. The collector gathers the electricity, water, heat, and energy consumption data through the RS485 field bus and stores the data into an SD card with mass storage, finally, using Internet to finish the communication and transmission to data server through TCP protocol. The collector has been used in application for two years, and the results show that the system is reliable and stable.

This paper gives a new prediction-correction method based on the dynamical system of differential-algebraic equations for the smallest generalized eigenvalue problem. First, the smallest generalized eigenvalue problem is converted into an equivalent-constrained optimization problem. Second, according to the Karush-Kuhn-Tucker conditions of this special equality-constrained problem, a special continuous dynamical system of differential-algebraic equations is obtained. Third, based on the implicit Euler method and an analogous trust-region technique, a prediction-correction method is constructed to follow this system of differential-algebraic equations to compute its steady-state solution. Consequently, the smallest generalized eigenvalue of the original problem is obtained. The local superlinear convergence property for this new algorithm is also established. Finally, in comparison with other methods, some promising numerical experiments are presented.

This paper investigates the problem of observer-based robust $H_{\infty }$ control for a class of switched stochastic systems with time-varying delay. Based on the average dwell time method, an exponential stability criterion for switched stochastic delay systems is proposed. Then, $H_{\infty }$ performance analysis and observer-based robust $H_{\infty }$ controller design for the underlying systems are developed. Finally, a numerical example is presented to illustrate the effectiveness of the proposed approach.

Optimal control for a family of systems in novel state derivative space form, abbreviated as SDS systems in this study, is proposed. The first step in deriving optimal control laws for SDS systems is to form an augmented cost functional. It turns out that novel differential Lagrange multipliers must be used to adjoin SDS system constraints (namely, the dynamical equations of the control system) to the integrand of the original cost functional which is a function of state derivatives. This not only eases our derivation but also makes our derivation parallel to that for systems in standard state space form. We will show via a real electric circuit that optimal control for a class of descriptor systems with impulse modes can easily be carried out using our design method. It will be shown that linear quadratic regulator (LQR) design for linear time-invariant SDS systems using state derivative feedback can be obtained via an algebraic Riccati equation. Furthermore, this optimal state derivative feedback may also be implemented using an equivalent state feedback. This is useful in real situations when only states but not the state derivatives are available for measurement. The LQR design for a double inverted pendulum system is implemented to illustrate the use of our method.

The study proposed the application of the fuzzy sliding mode for a gyroscope system status control. The state response analysis of the gyroscope system revealed highly nonlinear and chaotic subharmonic motions of $\mathrm{2T}$ during state formation. The current study discussed the use of tracking control on the sliding mode control and fuzzy sliding mode control of a gyroscope control system. Consequently, the gyroscope system drives from chaotic motion to periodic motion. The numerical simulation results confirm that the proposed controller provides good system stability and convergence without chattering phenomena.

The strapdown inertial navigation systems (SINS) have been widely used for many vehicles, such as commercial airplanes, Unmanned Aerial Vehicles (UAVs), and other types of aircrafts. In order to evaluate the navigation errors precisely and efficiently, a prediction method based on support vector machine (SVM) is proposed for positioning error assessment. Firstly, SINS error models that are used for error calculation are established considering several error resources with respect to inertial units. Secondly, flight paths for simulation are designed. Thirdly, the $\epsilon$-SVR based prediction method is proposed to predict the positioning errors of navigation systems, and particle swarm optimization (PSO) is used for the SVM parameters optimization. Finally, 600 sets of error parameters of SINS are utilized to train the SVM model, which is used for the performance prediction of new navigation systems. By comparing the predicting results with the real errors, the latitudinal predicting accuracy is 92.73%, while the longitudinal predicting accuracy is 91.64%, and PSO is effective to increase the prediction accuracy compared with traditional SVM with fixed parameters. This method is also demonstrated to be effective for error prediction for an entire flight process. Moreover, the prediction method can save 75% of calculation time compared with analyses based on error models.

Fuel cells (FCs) are characterized by low pollution, low noise, and high efficiency. However, the voltage-current response of an FC is nonlinear, with the result that there exists just one operating point which maximizes the output power given a particular set of operating conditions. Accordingly, the present study proposes a maximum power point tracking (MPPT) control scheme based on extension theory to stabilize the output of an FC at the point of maximum power. The simulation results confirm the ability of the controller to stabilize the output power at the maximum power point despite sudden changes in the temperature, hydrogen pressure, and membrane water content. Moreover, the transient response time of the proposed controller is shown to be faster than that of existing sliding mode (SM) and extremum seeking (ES) controllers.