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This paper addresses the invariant [ K , K L ] sector as a special class of [ K , K L ] sector that holds the invariant characteristics with some appropriate control input, i.e. the energy of the system drastically decreases and state trajectory always remains inside the sector once it moves into it by the suitable control signal. The analysis of the nonlinear sector is regarded in comparison function prospective to outreach the property of uniformity. Here, the construction of [ K , K L ] sector and invariant [ K , K L ] sector relies on the selection of well-suited control-Lyapunov function. The switching control with invariant [ K , K L ] sector is designed to ensure the state trajectories move inside the nonlinear sector in finite-time and stay inside for all future time. Finally, the effectiveness of the proposed algorithm is illustrated with real physical examples. [ABSTRACT FROM AUTHOR]

A Hands-off control law is investigated to asymptotically stabilize a nonlinear system with input-quantization. The quantization parameters generated at the coder and decoder sides of the communication channel are mismatched and a time-varying ratio is modeled to show the non-synchronous adjustment of the quantization parameters. By the means of $[\mathcal {K,KL}]$ sector, the state-space is roughly divided into an attractive and non-attractive regions and a controller based on On-Off logic is utilized to remove the model uncertainties caused by the mismatch of the quantization parameters with limited control effort. Finally, the illustration of the proposed scheme is verified for an electronic circuit. [ABSTRACT FROM AUTHOR]

This brief suggests an approach to design a robust ${[\mathcal {K,KL}]}$ sector for nonlinear system subjected to parametric/model uncertainty and this design relies on the Matrosov’s results. The nonlinear surface to decide the boundaries of a sector is designed by using a control-Lyapunov function. Here, a Hands-Off control consists of constant and state-dependent gain is used to force the state vectors to the interior of robust ${[\mathcal {K,KL}]}$ sector and shows asymptotic stability with minimum support to the nonlinear system by avoiding the redundant control effort. The usefulness of the proposed design is illustrated by a nonlinear electronic circuit. [ABSTRACT FROM AUTHOR]

Summary: This article presents a hands‐off control design for discrete‐time nonlinear system with a special type of nonlinear sector termed as "discrete‐time [𝒦,𝒦ℒ] sector." The design method to define the boundary of a discrete‐time [𝒦,𝒦ℒ] sector is done with control‐Lyapunov function. The generalization of nonlinear system is viewed in the perspective of a comparison function. By means of a proposed sector, a switching control is designed such that no control action is experienced inside the sector thus, saving unnecessary control efforts. However, to study the robustness for discrete‐time system, a hands‐off control is modified to ensure the monotonic decrease in the energy of the system. Finally, the proposed approach is verified with the simulation results. [ABSTRACT FROM AUTHOR]

A new approach for asymptotic stabilization of a general input-affine nonlinear system is presented. This relies upon the results of Matrosov's theorem to decompose the n th dimensional space. The construction of the [K,KL] sector for a nonlinear system is done with the suitable choice of control-Lyapunov function. The study of a nonlinear system is viewed from the perspective of comparison function for uniformity in solution. By means of designed sector, we design a switching controller which is well suited in the condition that shows its presence only outside of [K,KL] sector. Thus, it yields a stabilization scheme which saves the superfluous control termed as Lazy or Hands-Off control. Finally, we demonstrate the proposed approach which yields an asymptotically stable results for the simulation of an illustrative example. • The definition of [K,KL] sector with a K ∞ class function. • The equivalence definition of [K,KL] sector with the comparison of two K ∞ class functions. • The elementary [K,KL] sector based on the above equivalence definition. • The design specification of elementary [K,KL] sector. • A new approach to design [K,KL] sector. [ABSTRACT FROM AUTHOR]