State‐feedback stabilization for stochastic high‐order nonlinear systems with SISS inverse dynamics

This paper investigates the problem of state‐feedback control for a class of stochastic high‐order nonlinear systems with stochastic inverse dynamics. Under the assumption that the inverse dynamics of the subsystem are stochastic input‐to‐state stable (SISS), by extending through adding a power integrator technique, choosing an appropriate Lyapunov function and using the idea of changing supply function, a smooth state‐feedback controller is explicitly constructed to render the system globally asymptotically stable in probability and the states can be regulated to the origin. A simulation example is provided to show the effectiveness of the proposed scheme. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Finite‐time stabilization of stochastic nonlinear systems with SiISS inverse dynamics

This paper investigates the finite‐time control problem for a class of stochastic nonlinear systems with stochastic integral input‐to‐state stablility (SiISS) inverse dynamics. Motivated by finite‐time stochastic input‐to‐state stability and the concept of SiISS using Lyapunov functions, a novel finite‐time SiISS using Lyapunov functions is introduced firstly. Then, by adopting this novel finite‐time SiISS small‐gain arguments, using the backstepping technique and stochastic finite‐time stability theory, a systematic design and analysis algorithm is proposed. Given the control laws that guarantee global stability in probability or asymptotic stability in probability, our design algorithm presents a state‐feedback controller that can ensure the solution of the closed‐loop system to be finite‐time stable in probability. Finally, a simulation example is given to demonstrate the effectiveness of the proposed control scheme. Copyright © 2017 John Wiley & Sons, Ltd.     

State feedback stabilization of stochastic nonlinear systems with SiISS inverse dynamics

This paper further considers a more general class of stochastic nonlinear systems with stochastic integral input‐to‐state stability (SiISS) inverse dynamics and drift and diffusion terms depending upon the other states besides stochastic inverse dynamics and the first state. By skillfully choosing the designed functions and the update laws of parameters, and using the important mathematical tools established in IEEE Trans. Automat. Contr. 2010; 55 (2):304–320, a unifying framework of state feedback controller is proposed to guarantee that all the signals of the closed‐loop system are bounded almost surely and the states can be regulated to zero almost surely. A simulation example demonstrates the effectiveness of the control scheme. Copyright © 2011 John Wiley & Sons, Ltd.     

Finite‐time stabilization for a class of stochastic low‐order nonlinear systems with unknown control coefficients

This paper addresses the problem of finite‐time stabilization for a class of low‐order stochastic upper‐triangular nonlinear systems corrupted by unknown control coefficients. Unlike the relevant schemes, the control strategy draws into a dominate gain to cope with the deteriorative effects of both uncertain nonlinearities and unknown control coefficients without using traditional adaptive compensation method. Then, a state feedback controller is constructed by the adding a power integrator method and modified homogeneous domination approach, to ensure the finite‐time stability of the closed‐loop system. Finally, the effectiveness of proposed control strategy has been demonstrated by a simulation example.     

State‐feedback stabilization for high‐order stochastic nonlinear systems with stochastic inverse dynamics

For a class of high‐order stochastic nonlinear systems with stochastic inverse dynamics which are neither necessarily feedback linearizable nor affine in the control input, this paper investigates the problem of state‐feedback stabilization for the first time. Under some weaker assumptions, a smooth state‐feedback controller is designed, which ensures that the closed‐loop system has an almost surely unique solution on [0, ∞), the equilibrium at the origin of the closed‐loop system is globally asymptotically stable in probability, and the states can be regulated to the origin almost surely. A simulation example demonstrates the control scheme. Copyright © 2007 John Wiley & Sons, Ltd.     

Finite‐time output feedback stabilization of nonlinear high‐order feedforward systems

This paper considers the global finite‐time output feedback stabilization of a class of nonlinear high‐order feedforward systems. By using the homogeneous domination method together with adding a power integrator method and overcoming several troublesome obstacles in the design and analysis, a global finite‐time output feedback controller with reduced‐order observer is recursively designed to globally finite‐time stabilize nonlinear high‐order feedforward systems. Copyright © 2015 John Wiley & Sons, Ltd.     

Finite‐time stabilization of a class of switched stochastic nonlinear systems under arbitrary switching

This paper investigates the finite‐time stabilization of a class of switched stochastic nonlinear systems under arbitrary switching, where each subsystem has a chained integrator with the power r (0 < r < 1). By using the technique of adding a power integrator, a continuous state‐feedback controller is constructed, and it is proved that the solution of the closed‐loop system is finite‐time stable in probability. Two simulation examples are provided to show the effectiveness of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.     

Output feedback for stochastic nonlinear systems with unmeasurable inverse dynamics

This paper considers a concrete stochastic nonlinear system with stochastic unmeasurable inverse dynamics. Motivated by the concept of integral input-to-state stability （iISS） in deterministic systems and stochastic input-to-state stability （SISS） in stochastic systems, a concept of stochastic integral input-to-state stability （SiISS） using Lyapunov functions is first introduced. A constructive strategy is proposed to design a dynamic output feedback control law, which drives the state to the origin almost surely while keeping all other closed-loop signals almost surely bounded. At last, a simulation is given to verify the effectiveness of the control law.     

Finite‐time stabilization for a class of switched stochastic nonlinear systems with dead‐zone input nonlinearities

This paper studies the finite‐time stabilizing control problem for a class of switched stochastic nonlinear systems (SSNSs) in p‐normal form. The switched systems under consideration possess the powers of different positive rational numbers and the dead‐zone input nonlinearities. Based on the improving finite‐time stability theorem for SSNSs established in this paper, a general framework to address common state feedback for SSNSs is developed by adopting the common Lyapunov function–based adding a power integrator technique. It is proved that the proposed controller renders the trivial solution of the closed‐loop system uniformly finite‐time stable in probability under arbitrary switchings. Finally, simulation results are given to confirm the validity of the proposed approach.     

Finite‐time output‐feedback stabilization of high‐order nonholonomic systems

This paper investigates the problem of finite‐time output‐feedback stabilization of a class of high‐order nonholonomic systems under weaker conditions on system powers and nonlinearities. By constructing the appropriate Lyapunov function and observer, skillfully combining generalized adding a power integrator technique, sign function, and homogeneous domination method, and successfully introducing a new mathematical method, an output‐feedback controller is constructed to guarantee that all the states of the closed‐loop system converge to origin in a finite time.     

State feedback control of a class of high‐order stochastic nonlinear systems

This paper poses and solves a new problem of state feedback stabilization for a class of high‐order stochastic nonlinear systems in which the power order restriction and growth condition are relaxed to a more general form. Based on the ideas of the homogeneous systems theory and the adding of a power integrator technique, a state feedback controller is constructed to ensure that the equilibrium at the origin of the closed‐loop system is globally asymptotically stable in probability and that the problem of inverse optimal stabilization in probability is solved. The efficiency of the state feedback controller is demonstrated by a simulation example. Copyright © 2011 John Wiley & Sons, Ltd.     

Continuous finite‐time state feedback stabilizers for some nonlinear stochastic systems

This paper is concerned with the problem of finite‐time stabilization for some nonlinear stochastic systems. Based on the stochastic Lyapunov theorem on finite‐time stability that has been established by the authors in the paper, it is proven that Euler‐type stochastic nonlinear systems can be finite‐time stabilized via a family of continuous feedback controllers. Using the technique of adding a power integrator, a continuous, global state feedback controller is constructed to stabilize in finite time a large class of two‐dimensional lower‐triangular stochastic nonlinear systems. Also, for a class of three‐dimensional lower‐triangular stochastic nonlinear systems, a recursive design scheme of finite‐time stabilization is given by developing the technique of adding a power integrator and constructing a continuous feedback controller. Finally, a simulation example is given to illustrate the theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

Stability and stabilization of nonlinear discrete‐time stochastic systems

This paper mainly studies the locally/globally asymptotic stability and stabilization in probability for nonlinear discrete‐time stochastic systems. Firstly, for more general stochastic difference systems, two very useful results on locally and globally asymptotic stability in probability are obtained, which can be viewed as the discrete versions of continuous‐time Itô systems. Then, for a class of quasi‐linear discrete‐time stochastic control systems, both state‐ and output‐feedback asymptotic stabilization are studied, for which, sufficient conditions are presented in terms of linear matrix inequalities. Two simulation examples are given to illustrate the effectiveness of our main results.     

Finite‐Time Stabilization of Stochastic High‐Order Nonlinear Systems

This paper considers the problem of global finite‐time stabilization in probability for stochastic high‐order nonlinear systems in which the power order is greater than or equal to one and the drift and diffusion terms satisfy weaker growth conditions. Based on stochastic Lyapunov theorem on finite‐time stability, via the combined adding one power integrator and sign function method, constructing a Lyapunov function and verifying the existence and uniqueness of solution, a continuous state feedback controller is designed to guarantee the closed‐loop system globally finite‐time stable in probability.     

A dual‐observer design for global output feedback stabilization of nonlinear systems with low‐order and high‐order nonlinearities

This paper employs a dual‐observer design to solve the problem of global output feedback stabilization for a class of nonlinear systems whose nonlinearities are bounded by both low‐order and high‐order terms. We show that the dual‐observer comprised of two individual homogeneous observers, can be implemented together to estimate low‐order and high‐order states in parallel. The proposed dual observer, together with a state feedback controller, which has both low‐order and high‐order terms, will lead to a new result combining and generalizing two recent results (Li J, Qian C. Proceedings of the 2005 IEEE Conference on Decision and Control, 2005; 2652–2657) and (Qian C. Proceedings of the 2005 American Control Conference, June 2005; 4708–4715). Copyright © 2008 John Wiley & Sons, Ltd.     

Finite‐time stability and stabilization of semi‐Markovian jump systems with time delay

Semi‐Markovian jump systems are more general than Markovian jump systems in modeling practical systems. On the other hand, the finite‐time stochastic stability is also more effective than stochastic stability in practical systems. This paper focuses on the finite‐time stochastic stability, exponential stochastic stability, and stabilization of semi‐Markovian jump systems with time‐varying delay. First, a new stability condition is presented to guarantee the finite‐time stochastic stability of the system by using a new Lyapunov‐Krasovskii functional combined with Wirtinger‐based integral inequality. Second, the stability criterion is further proved to guarantee the exponential stochastic stability of the system. Moreover, a controller design method is also presented according to the stability criterion. Finally, an example is provided to illustrate that the proposed stability condition is less conservative than other existing results. Additionally, we use the proposed method to design a controller for a load frequency control system to illustrate the effectiveness of the method in a practical system of the proposed method.     

Output‐feedback control of a class of stochastic nonlinear systems with linearly bounded unmeasurable states

In this paper, the problems of stochastic disturbance attenuation and asymptotic stabilization via output feedback are investigated for a class of stochastic nonlinear systems with linearly bounded unmeasurable states. For the first problem, under the condition that the stochastic inverse dynamics are generalized stochastic input‐to‐state stable, a linear output‐feedback controller is explicitly constructed to make the closed‐loop system noise‐to‐state stable. For the second problem, under the conditions that the stochastic inverse dynamics are stochastic input‐to‐state stable and the intensity of noise is known to be a unit matrix, a linear output‐feedback controller is explicitly constructed to make the closed‐loop system globally asymptotically stable in probability. Using a feedback domination design method, we construct these two controllers in a unified way. Copyright © 2007 John Wiley & Sons, Ltd.     

Multirate sampled‐data stabilization for a class of low‐order lower‐triangular nonlinear systems

This paper investigates the problem of sampled‐data controller design for a class of lower‐triangular systems in the p‐normal form (0<p<1). A multirate digital feedback control scheme is proposed to achieve the global strong stabilization of the sampled‐data closed‐loop system under some assumptions. In the design of the controller, the input‐Lyapunov matching strategy and multirate control approach are combined to obtain better stabilizing performance. Unlike the design method based on the approximate discrete‐time model, our controller is obtained from the exact discrete‐time equivalent model, which does not need to be computed completely. The approximate multirate digital controllers are proved to be effective in the practical implementation. It is shown that, compared with the emulated control scheme, our controller may provide faster decrease of Lyapunov function for each subsystem. This will lead to allow large sampling periods. An illustrative example is provided to verify the effectiveness of the proposed control scheme.     

Input‐to‐state stability of nonlinear stochastic time‐varying systems with impulsive effects

This paper considers the input‐to‐state stability, integral‐ISS, and stochastic‐ISS for impulsive nonlinear stochastic systems. The Lyapunov function considered in this paper is indefinite, that is, the rate coefficient of the Lyapunov function is time‐varying, which can be positive or negative along time evolution. Lyapunov‐based sufficient conditions are established for ensuring ISS of impulsive nonlinear stochastic systems. Three examples involving one from networked control systems are provided to illustrate the effectiveness of theoretical results obtained. Copyright © 2016 John Wiley & Sons, Ltd.     

Finite‐time robust simultaneous stabilization of a set of nonlinear time‐delay systems

This paper investigates the finite‐time robust simultaneous stabilization problem of a set of nonlinear time‐delay systems with general forms and proposes some new simultaneous stabilization results. First, by developing an equivalent form and applying augmented technique, this paper obtains an augmented equivalent form of the original systems. Secondly, based on the equivalent form, we study finite‐time simultaneous stabilization problem and present some new stabilization results by constructing some suitable Lyapunov functionals. Thirdly, using the simultaneous stabilization results obtained, this paper investigates the finite‐time robust simultaneous stabilization problem for the set systems and proposes a delay‐dependent robust simultaneous stabilization result. Finally, the study of an illustrative example shows that the results obtained by this paper work well in the finite‐time robust simultaneous stabilization the set systems. It is shown that, by using the method in this paper, the developed conditions do not contain delay terms, which can avoid solving nonlinear mixed matrix inequalities and reduce effectively computational burden in studying nonlinear time‐delay systems.