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Global sampled‐data stabilization for a class of nonlinear continuous system with input delay has been investigated directly in the discrete‐time domain due to challenges confronted in dealing with infinite‐dimensional system under input delay. Memorized state feedback controllers and output feedback controllers based on dynamic extension of state space have been constructed within the framework of co‐design between sampling period and scaling gain. Upon this compensation scheme, global sampled‐data stabilization a class of nonlinear system has been successfully realized no matter the input delay is smaller than the sampling period or not. Compared with memory‐less sampled‐data controllers, not only sampled‐data stabilization under large input delay has been realized but also transient performance of closed‐loop system has been further improved. Simulation results under different input delays and sampling periods have illustrated the effectiveness of results obtained. [ABSTRACT FROM AUTHOR]

Summary: This paper proposes some novel compensating strategies in output feedback controller design for a class of nonlinear uncertain system. With Euler approximation introduced for unmeasured state and coordinate transformation constructed for continuous system, sampled‐data stabilization under arbitrary sampling period is firstly realized for linear system using compensation between sampling period and scaling gain. Then global sampled‐data stabilization for a class of nonlinear system is studied using linear feedback domination of Lyapunov functions. Extension of obtained results to three‐dimensional system or systems under general assumptions are also presented. With the compensation schemes proposed in controller design, the sufficiently small sampling period or approximating step previously imposed is not required any more. The proposed controllers can be easily implemented using output measurements sampled at the current step and delayed output measurements sampled at the previous step without constructing state observers which has been illustrated by the numerical studies. [ABSTRACT FROM AUTHOR]

We present a nonsmooth output feedback framework for local and/or global stabilization of a class of nonlinear systems that are not smoothly stabilizable nor uniformly observable. A systematic design method is presented for the construction of stabilizing, dynamic output compensators that are nonsmooth but Holder continuous. A new ingredient of the proposed output feedback control scheme is the introduction of a recursive observer design algorithm, making it possible to construct a reduced-order observer step-by-step, in a naturally augmented manner. Such a nonsmooth design leads to a number of new results on output feedback stabilization of nonlinear systems. One of them is the global stabilizability of a chain of odd power integrators by Holder continuous output feedback. The other one is the local stabilization using nonsmooth output feedback for a wide class of nonlinear systems in the Hessenberg form studied in a previous paper, where global stabilizability by nonsmooth state feedback was already proved to be possible. Index Terms--Homogeneous approximation, nonlinear systems, nonsmooth observers, nonsmooth stabilizability, nonuniform observability, output feedback stabilization.

This note studies the problem of global finite-time stabilization by dynamic output feedback for a class of continuous but nonsmooth nonlinear systems. By extending the adding-a-power-integrator technique and a special continuous observer design, a dynamic output feedback controller is explicitly constructed to render the systems globally finite-time stable. The novelty of the note is the development of a recursive design procedure, which takes full advantage of the continuous structure of the systems in constructing the state feedback stabilizer and the continuous observer with rigorously selected gains. Index Terms--Continuous nonlinear systems, global finite-time stabilization, output feedback control.

This note considers the problem of global finite-time stabilization by output feedback for a class of planar systems without controllable/observable linearization. A sufficient condition for the solvability of the problem is established. By developing a nonsmooth observer and modifying the adding a power integrator technique, we show that an output feedback controller can be explicitly constructed to globally stabilize the systems in finite time. As a direct application of the main result, global output feedback finite-time stabilization is achieved for the double linear integrator systems perturbed by some nonlinear functions which are not necessarily homogeneous. Index Terms--Finite-time stabilization, nonlinear systems, output feedback, unobservable linearization.

This brief deals with the problem of semi-global stabilization by output feedback for a class of uncertain nonlinear systems. Due to the presence of mismatched uncertainties and the lack of triangularity condition, the systems under consideration are not uniformly completely observable. In addition, the uncertain nonlinear dynamics of the systems are higher order, rather than linearly growing, in the unmeasurable states. All these make the systems not semi-globally stabilizable by the existing output feedback design schemes. In this brief, by extending the feedback domination design techniques proposed by Qian and Lin, a systematic design scheme is developed to construct linear output feedback controllers that semi-globally stabilize a general class of uncertain nonlinear systems under less restrictive conditions. Index Terms--Nonlinear systems, observer design, output feedback, semi-global stabilization.

This article investigates the fixed‐time stabilization problem for a class of high‐order nonlinear systems with monotone degrees and output constraints. Firstly, a new fixed‐time stability criterion is established, which is less conservative in the explicit and delicate selection of Lyapunov functions. Then, by choosing a novel tan‐type barrier Lyapunov function (BLF) and using the generalized adding a power integrator (AAPI) technique, a fixed‐time stabilization controller is explicitly constructed while achieving the requirement of state constraints. The novelty of the proposed control strategy can tackle simultaneously the fixed‐time stabilization of the involved systems with and without output constraints, without changing the controller structure. A simulation example is given to show the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

This note considers the problem of global stabilization by output feedback for a family of planar systems whose Jacobian linearization is neither controllable nor observable. The problem cannot be dealt with by existing output feedback design methods--most of them are based on the separation principle. Under appropriate growth conditions, we propose an output feedback control scheme that does not rely on the separation principle and achieves global asymptotic stabilization. The novelty of our control scheme lies in the explicit design of a dynamic output compensator, which combines a nonlinear-gain observer design and the technique of adding a power integrator. As a consequence, an interesting global stabilization result by output feedback can be obtained for feedback linearizable systems in a triangular form, which turns out to be new even in the two-dimensional case. Index Terms--Global stabilization, nonseparation principle design, planar systems, smooth output feedback, uncontrollable/unobservable linearization.

This note considers the problem of global stabilization by output feedback, for a family of nonlinear systems that are dominated by a triangular system satisfying linear growth condition. The problem has remained unsolved due to the violation of the commonly assumed conditions in the literature. Using a feedback domination design method which is not based on the separation principle, we explicitly construct a linear output compensator making the closed-loop system globally exponentially stable. Index Terms--Global robust stabilization, linear growth condition, nonlinear systems, nonseparation principle design, output feedback.

This paper studies global adaptive control of nonlinearly parameterized systems with uncontrollable linearization. Using a new parameter separation technique and the tool of adding a power integrator, we develop a feedback domination design approach for the explicit construction of a smooth adaptive controller that solves the problem of global state regulation. In contrast to the existing results in the literature, a key feature of our adaptive regulator is its minimum-order property, namely, no matter how big the number of unknown parameters is, the order of the dynamic compensator is identical to one, and is therefore minimal. As a consequence, global state regulation of feedback linearizable systems with nonlinear parameterization is achieved by one-dimensional adaptive controllers, without imposing any extra (e.g., convex/concave) conditions on the unknown parameters. Index Terms--Adding a power integrator, global adaptive stabilization, nonlinear parameterization, nonlinear systems with uncontrollable linearization, smooth feedback.

This paper introduces a nonsmooth framework for global adaptive control of a significant class of nonlinearly parameterized systems with uncontrollable unstable linearization. While there may not exist any smooth static or dynamic stabilizer due to the violation of the well-known necessary condition, we give sufficient conditions for the existence of non-Lipschitz continuous adaptive regulators that achieve global stability with asymptotic state regulation. A constructive design method is developed based on an effective coupling of a new parameter separation technique and the tool of adding a power integrator, leading to [C.sup.o] adaptive regulators with minimal parameterization. Indeed, the dimension of the proposed dynamic compensator can always be one, irrespective of the number of unknown parameters. The power of our continuous adaptive control strategy is demonstrated by solving a number of challenging adaptive stabilization problems that have remained open for more than a decade. Index Terms--Adding a power integrator, global adaptive regulation, nonlinear parameterization, nonlinear systems, nonsmooth adaptive controller, uncontrollable unstable linearization.

We address the problems of almost asymptotic stabilization and global asymptotic regulation (GAR) for a class of high-order nonholonomic systems in power chained form. This particular class of nonlinear systems is an extension of a nonholonomic system in chained form that has received considerable attention in the past few years. The nonholonomic system considered in this note is not necessarily affine in the control variables and therefore cannot be handled by existing methods. Sufficient conditions are presented under which a discontinuous state feedback control law (respectively, a switching controller) can be recursively constructed, using the so-called adding a power integrator technique proposed in [17], [18]. We also illustrate how the results can be extend to multi-input systems in power chained form. Simulation examples are provided to demonstrate effectiveness of the proposed controllers. Index Terms--Adding a power integrator, discontinuous state feedback, global asymptotic regulation, high-order nonlinear systems, power chained form.