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When we study the Karnaugh map in the switching theory course, we learn that the ones in the map are combined in rectangles whose length and width must be a power of two. The result is the logic function described as a sum of products. This paper shows that we can also make groups where the length and width of the rectangles are equal to three. This results in a logic function that is simpler than the sum of products in terms of logic gates, leading to more hardware-efficient circuits. This idea is extended later in the paper to other groups of elements. Finally, a new perspective on the Karnaugh map that integrates the proposed approach with the conventional one is provided. This can be used in switching theory courses to improve the explanation of the Karnaugh map. [ABSTRACT FROM AUTHOR]

The paper studies the problem of asymptotically stabilizing a class of switched linear neutral systems, where none of the individual subsystems is stabilizable. A co-design of a set of candidate controllers and a hysteresis-based switching strategy is developed to achieve asymptotic stability of the closed-loop switched neutral systems. Finally, a numerical example is given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, the problems of stability and stabilization for switched systems with mode-dependent average dwell time (MDADT) switching are revisited and discussed in both continuous-time and discrete-time contexts. By introducing a class of quasi-alternative switching signals, some improved stability conditions of switched systems with MDADT are obtained. In our switching design strategy, slow switching and fast switching are, respectively, used among stable subsystems and unstable subsystems. Then, based on the stability result, stabilization conditions for switched linear systems comprising uncontrollable subsystems are presented to guarantee the underlying system to be exponentially stable. The criteria obtained for the considered switched linear systems are all provided in terms of a set of linear matrix inequalities. To illustrate the advantages of our established results, a numerical example is finally given. [ABSTRACT FROM AUTHOR]

In this paper, the problem of adaptive control for a class of continuous-time switched linear systems is studied using a state-dependent switching method. All subsystems of the switched system under study can be unstable. First, an adaptive controller and a variable structure (VS) switching law with sliding sector are proposed, and some conditions are established in terms of linear matrix inequalities to guarantee the underlying system to be asymptotically stable. Then the problem of robust $$H_{\infty }$$ control for the systems under study is also solved by designing a proposed adaptive controller and a VS switching law. Finally, a numerical example is given to demonstrate the effectiveness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This paper focuses on the hybrid effects of Markovian switching, stochastic perturbation, and impulsive delay on neural networks. First, some novel generic criteria for Markovian switching neural networks with stochastic perturbation and impulsive delay are derived by establishing an extended Halanay differential inequality on impulsive dynamical systems. Second, our sufficient conditions ensuring synchronization are dependent on coupling and impulsive delay, and show coupling and impulsive effects on the synchronization of neural networks. Finally, simulation results demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the fault detection (FD) problem for a class of linear discrete-time switched systems in finite-frequency domain. The fault detection filters (FDFs) with switching mechanism are utilized to generate residual to detect fault. Different from the existing FD schemes based on the arbitrary switching or average dwell time switching method, a novel scheme is presented, where the states of the FDFs are used to construct not only the residual but also the switching law. This guarantees that the overall switched system is asymptotically stable and with the fault sensitive performance and disturbance attenuation performance in the low-, middle-, and high-frequency domain, respectively. A solution of the considered problem is given via linear matrix inequalities. Finally, a numerical example is presented to show the advantage of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, a switching strategy for recursive fractional variable-order derivative is proposed. This strategy can be interpreted as an explanation of order switching mechanism for this particular type of derivative. Additionally, important properties of variable fractional order derivatives, required for prove the main result, are introduced both in a difference equation and a matrix form. Duality between the recursive and standard variable-order derivative is detailed derived. Based on the switching scheme, an analog realization of the recursive variable-order derivative definition is presented. Experimental results obtained for the analog realization are compared to the numerical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the output feedback passification of switched continuous-time linear systems with actuation saturation. A switching law and saturated output feedback controllers with the form of quasi-linear parameter-varying are designed such that the closed-loop switched system with actuator saturation is passive, and the system state remains inside an invariant ellipsoid, which meet the requirements of passivity and saturation simultaneously. Since the system state is often unavailable, we consider the issue of how to design dynamic output feedback controllers using only partial state measurements. Moreover, the switching law is designed to depend only on the state of the dynamic output feedback controllers, which renders the switched system passivity even the subsystems are non-feedback passive. Sufficient conditions for the existence of the switching and output feedback control law are derived in terms of linear matrix inequalities. Finally, a numerical example is given to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper considers the stabilization problem for a class of cascade switched nonlinear systems. Each subsystem of the switched nonlinear system studied consists of a linear part and a nonlinear part, and the linear parts are composed of stabilizable and unstabilizable subsections. The actuator saturation is taken into consideration using the convex hull technique. Through constructing the proper Lyapunov functions, sufficient conditions in terms of LMIs for the solvability of the stabilization problem are presented. A state feedback controller and the dwell-time switching strategy are proposed to guarantee the exponential stability of the resulting closed-loop system. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]