On Stochastic Finite-Time Stabilization with Continuous State-Feedback Controllers

The problems of robust finite-time stochastic stability and stabilization of uncertain networked control systems (NCSs) in the presence of random delays are considered in this paper. First, network-induced random delays are modeled as a Markov chain, and the resulting closed-loop system is transformed into a Markovian jump linear system (MJLS). Since the accurate access to the transition probabilities (TPs) is hard or even impossible, some of the elements in the transition probability matrix (TPM) are considered as unknown parameters. Based on this model, the sufficient conditions for the robust finite-time stochastic stability and stabilization of the uncertain NCS are proposed. Moreover, a new linear matrix inequality (LMI) approach is employed to calculate the static output-feedback controllers. Additionally, the results of the proposed scheme are verified by two examples and simulations, which include a practical example.

In this paper, stochastic finite-time stability analysis and stabilization problems for stochastic delayed recurrent neural networks(SDRNNs) are investigated, and the stochastic settling time function is also estimated. The sufficient condition of stochastic finite-time stable(SFTS) for SDRNNs is proposed at first. Then the nonlinear delay-feedback controller to stochastic finite-time stabilize the SDRNNs is designed. Finally, an numerical example is given to show the corrections of the proposed results and the effectiveness of the provided controller.

This paper discusses the problem of global finite-time stabilization in probability for a class of stochastic high-order nonlinear systems whose drift and diffusion terms satisfy lower-triangular growth conditions. By adopting adding one power integrator technique and constructing twice continuous differential Lyapunov functions, a continuous state-feedback controller is recursively designed. Based on stochastic finite-time stability theorem, it is proved that the solution of the closed-loop system is finite-time stable in probability. Several simulation examples are given to illustrate the effectiveness of the proposed design procedure.

In this paper, a suite of theoretic tools is provided for discontinuous control design and finite-time stability analysis of a class of stochastic differential systems. The notion of Filippov&#x0027;s solutions for stochastic differential systems is proposed, and the corresponding solution existence problem is explored. The classical It&#x00F4; differentiation formula is generalized for quasi-<inline-formula><tex-math notation="LaTeX">$C_{0}^{2}(\mathbb {R}^{n},\mathbb {R})$</tex-math></inline-formula>-class functions along Filippov&#x0027;s solutions of stochastic differential systems, and two involved set-valued stochastic integrals are introduced with a study on their properties. Some finite-time stability results of stochastic differential systems are revealed with Filippov&#x0027;s solutions, and one of them is applied to neural synchronization, together with case simulations.

This paper investigates the problems of finite-time stability and finite-time stabilization for nonlinear quadratic systems with jumps. The jump time sequences here are assumed to satisfy some given constraints. Based on Lyapunov function and a particular presentation of the quadratic terms, sufficient conditions for finite-time stability and finite-time stabilization are developed to a set containing bilinear matrix inequalities (BLIMs) and linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the proposed methodology.

Finite-time stability and stabilization of linear discrete time-varying stochastic systems

This chapter extends the results of finite-time controller design to discrete-time switching Markovian jump systems with time-delay. Considering the effect of the average dwell time on the finite-time performance, some results on the stochastic finite-time boundedness and stochastic finite-time stabilization with\(H_\infty \) disturbance attenuation level are given, and the relationship among three kinds of time scales, such as time-delay, average dwell time and finite-time interval, are derived by means of the average dwell time constraint condition.

This paper deals with the finite-time stabilization problem for discrete-time Markov jump nonlinear systems with time delays and norm-bounded exogenous disturbance. The nonlinearities in different jump modes are parameterized by neural networks. Subsequently, a linear difference inclusion state space representation for a class of neural networks is established. Based on this, sufficient conditions are derived in terms of linear matrix inequalities to guarantee stochastic finite-time boundedness and stochastic finite-time stabilization of the closed-loop system. A numerical example is illustrated to verify the efficiency of the proposed technique.

H finite-time control for switched nonlinear discrete-time systems with norm-bounded disturbance

This paper investigates the problem of finite-time state feedback stabilization for nonholonomic mobile robot with stochastic disturbance in the forward velocity. First of all, an appropriate state/input transformation is introduced to convert the mentioned control model into stochastic nonholonomic system in chain form. Then, by using stochastic finite-time stability theorem and the method of adding a power integrator, a state feedback controller is obtained. Based on switching strategy to eliminate the phenomenon of uncontrollability, the proposed controller can guarantee that the closed-loop system is globally finite-time regulated at origin in probability. A simulation example is finally provided to demonstrate the validness of the proposed approach.

Finite-time stabilization of linear systems by bounded event-triggered and self-triggered control

The finite-time stabilization and robust control of stochastic nonlinear systems was discussed in this paper. First, by transforming the considered system to its equivalent Hamiltonian system, we showed that the stochastic dissipative Hamiltonian system was finite-time stable in probability if the Hamiltonian function and internal damping matrix possessed some structures. Then, we utilized the energy shaping and damping injection techniques to reformulate the internal structures and Hamiltonian function of the stochastic Hamiltonian system and constructed a finite-time stabilization controller. Finally, a robust finite-time controller was put forward for uncertain stochastic nonlinear systems by using the Hamiltonian function to construct a solution of Hamiltonian-Jacobi Inequality. Numerical simulations results demonstrated the effectiveness of the proposed stabilization and robust stabilization methods.

We consider the problem of finite-time stabilization for nonlinear systems. In the previous work, it was proved that global finite-time stabilizability of uncertain nonlinear systems that are dominated by a lower-triangular system could be achieved by non-Lipschitz continuous state feedback. The proof was based on the finite-time Lyapunov stability theorem and the nonsmooth feedback design method proposed in, for the control of nonlinear systems that are impossible to be dealt with by any smooth feedback. A simpler design algorithm is given for the construction of a non-Lipschitz continuous, global finite-time stabilizer as well as a C/sup 1/ positive definite and proper Lyapunov function that guarantees finite-time stability.

This paper investigates the problem of parameter-dependent state feedback control of continuous-time systems in the context of finite time stability. The controller is designed in order to guarantee that the closed-loop system is finite time stable. The system is considered time varying with the parameters modeled within a unit simplex. The design conditions obtained by means of Lyapunov functions are expressed as linear matrix inequalities. The finite time stability is assessed by using homogeneous polynomially parameter-dependent state feedback gains with arbitrary degree g. LMI relaxations are proposed based on Pólya's theorem. A controller is obtained by the solution of a factibility problem and the effect of the relaxation procedures analyzed by an optimization problem. Numerical examples are provided.

Finite time stability and stabilization of hybrid dynamic systems