1549-7747 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TCSII.2021.3120651, IEEE Transactions on Circuits and Systems II: Express Briefs 1 A [K, KL] sector based Hands-off control with quantization parameter mismatch Ankit Sachan, Sharat Chandra Mahto, Vijay Kumar Singh, Shyam Kamal, Thach Ngoc Dinh Abstract—A Hands-off control law is investigated to asymptot- ically 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 modelled to show the non-synchronous adjust- ment of the quantization parameters. By the means of [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. Index Terms—[K, KL] sector, Hands-off control, input- quantization, asymptotic stability. I. I NTRODUCTION Hands-off control [1] is a paradigm of variable structure control which shows a switching action between an open-loop structure and a closed-loop structure of the dynamical system. This equips with a minimum assistance to govern the state towards a stable region. However, the switching criterion of event-triggered control [2] is much likely similar to that of Hands-off control but the main difference is that the state vectors are continuously monitored and the control signal is only updated when its value crosses a certain threshold value obtained from its previous sampled value. More likely, the execution of event-triggered control is done in aperiodic manner and some work refered in [3]–[5]. By the means of Matrosov’s proof [6], the state-space is roughly divided into an attractive and non-attractive regions depending upon the sign- definiteness of the derivative of Lyapunov-candidate function. Intitutively, some difficulty appears in the construction of an attractive region for nonlinear system because there is no general procedure to find an appropriate Lyapunov func- tion and one should decide by trial and error method. This construction led significant amount of work to recall Zubov method [7] where the Lyapunov function approaches the value 1 on the boundary of attractive region. The computational advantage for this procedure is that the information about the solution is not required. An approach for computing control- Lyapunov function was first introduced by Sontag in [8] which results a universal formula for feedback stabilization. This procedure avoids the dependability of the system to solve for an algebraic/differential Riccati equation [9] for the considered system to decide the boundary of a sector. In order to design an attractive region for nonlinear system, a [K, KL] sector is proposed in [10], [11] and its boundary to seperate the regions is decided by a control-Lyapunov function [12]. Here, the Hands-off control seems to perform a switching action to ensure the system stability. Moreover, some additional developments are made in the direction of robustness analysis for nonlinear sector design as in [13], [14]. In modern engineering systems, signal quantization is an ongoing research topic due to wide applications of communi- cation channels with information processing units, see [15]– [17] and references therein. Among these research articles, the important aspect is the quantization of state signal is done before the design of feedback control design. For example, for nonlinear complex system in the busty fading channels, the event-triggering based control law is investigated in [18]. However, the communication saving for complex system is done by integrating the quantization approach with event- based scheme [20]. In addition, in [19], quantized-feedback control for nonlinear system with nonlinear sector design was investigated. In general, the quantization parameters cultivated at both the ends of the communication channel are assumed to be identical. But the discrepancy of quantization parameter oc- curs because of hardware imperfections and firstly investigated in [21]. Similar discussion to provide the stability conditions for the nonlinear system with encoder/decoder mismatch are attained in [22], [23]. While analyzing the inconsistency in quantization parameters of coder and decoder, its ratio is needed to remain unchanged by adjusting the synchronization of quantization parameters of coder and decoder at every time- instant. The above discussion motivate us to study mismatch relation between quantization parameter of coder and decoder sides for nonlinear system dealing with [K, KL] sector. In this paper, a Hands-off control is designed for the mismatched relation between the quantization parameter of coder and decoder ends of communication channel. The main contribution includes threefolds. First, a [K, KL] sector is designed for the nonlinear system within the n th -dimensional space. Second, a time-varying ratio is modeled for showing the mismatched relation of the quantization parameters at the coder and decoder sides. Third, a controller based on On-Off logic is utilized to remove the effect of model uncertainties appeared while the input-quantization. Thus, the closed-loop system acquires asymptotic stability. II. SYSTEM DESCRIPTION Consideration of nonlinear-affine system with quantized input in the form of state-space equation as follows: ˙ ζ = F (ζ )+ G(ζ )Q(u(t)) (1) where the functions F (ζ ) and G(ζ ) are C 1 continuously differentiable and maps F,G : Z→ R n where a domain Z