Finite-time stability and stabilization of nonlinear singular time-delay systems via Hamiltonian method

Passivity-based sliding mode control of uncertain singular time-delay systems

A novel theorem for prescribed-time control of nonlinear uncertain time-delay systems

In this paper, we consider the problem of finite-time stability for a class of linear singular time-delay systems. New delay dependent stability conditions have been derived using the approach based on the Lyapunov-like functions and their properties on the subspace of consistent initial conditions. The stability conditions are presented in the form of linear matrix inequalities. A numerical example has been provided to show the advantage of derived results.

This paper provides sufficient conditions for both practical stability and finite time stability of linear singular continuous time delay systems which can be mathematically described as Eẋ(t) = A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> x(t) + A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> x(t - τ). Considering a finite time stability concept, new delay independent conditions have been derived using the approach based on the Lyapunov-like functions and their properties on the subspace of consistent initial conditions. These functions do not need to have the properties of positivity in the whole state space and negative derivatives along the system trajectories. When the practical stability has been analyzed the above mentioned approach was combined and supported by the classical Lyapunov technique to guarantee the attractivity property of the system behavior.

The issue of exponential stability of a class of continuous-time switched nonlinear singular systems consisting of a family of stable and unstable subsystems with time-varying delay is considered in this paper. Based on the free-weighting matrix approach, the average dwell-time approach and by constructing a Lyapunov-like Krasovskii functional, delay-dependent sufficient conditions are derived and formulated to check the exponential stability of such systems in terms of linear matrix inequalities (LMIs). By checking the corresponding LMI conditions, the average dwell-time and switching signal conditions are obtained. This paper also highlights the relationship between the average dwell-time of the switched nonlinear singular time-delay system, its stability and the exponential convergence rate of differential and algebraic states. A numerical example shows the effectiveness of the proposed method.

This paper focuses on finite-time robust adaptive simultaneous stabilisation for nonlinear time-delay systems, taking into account actuator saturation and unknown parameters. Firstly, by employing adaptive control strategies and finite-time stability theory, a finite-time adaptive simultaneous stabilisation scheme for the nonlinear time-delay systems is developed. Secondly, utilising the orthogonal decomposition method, a finite-time robust adaptive simultaneous stabilisation scheme for nonlinear time-delay systems with external disturbances is proposed. Finally, simulations demonstrate the effectiveness of the provided control scheme.

In this paper, the finite-time stability and control of a kind of singular bio-economic systems with stochastic fluctuations are investigated. When economic profit is no longer a constant but a variable, the system shows distinct dynamic behavior. First, a singular system is proposed to describe the bio-economic system with stochastic fluctuation. Then a singular stochastic T-S fuzzy model is established based on T-S fuzzy system theory. Second, a sufficient condition is proposed to satisfy finite-time stochastic stability of bio-economic system. On this basis, a fuzzy state feedback controller is designed which can make corresponding closed-loop singular stochastic bio-economic system admissible in finite-time, and the states of the system can be driven to a bounded range through the management of the open resource. Finally, the validity of the results is verified through the numerical simulation.

This paper is concerned with robust passivity analysis of a class of uncertain nonlinear singular time-delay systems as well as with passivity-based sliding mode control of such systems. First we derive a delay-dependent sufficient condition expressed by means of linear matrix inequalities for achieving the generalized quadratic stability and robust passivity of the sliding mode dynamics. Then we show that the system's trajectories can be driven onto the pre-defined switching surface in a finite through synthesis of a sliding mode control law. Finally we present a numerical example that demonstrates the applicability of the derived theoretical results.

ROBUST OUTPUT REGULATION OF SINGULAR NONLINEAR SYSTEMS

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.

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

This paper is concerned with the problem of designing output feedback controller and guaranteed cost controller of discrete-time singular piecewise-affine systems with time delay and norm-bounded time-varying parameters uncertainties. Firstly, the corresponding operating region of the time-delay singular piecewise-affine systems in state space is described as ellipsoid which can be solved by a set of vector inequalities. Then, based on a singular piecewise Lyapunov-Krasovskii function combined with S-procedure and some matrix inequality convexifying techniques, the output feedback controller of the time-delay singular systems is investigated, and meanwhile, the guaranteed cost controller of the time-delay singular piecewise-affine systems is solved in terms of linear matrix inequalities (LMIs). It is shown that the controller gains can be obtained by solving a family of LMIs parameterized by one or two scalar variables. Numerical examples are given to illustrate the effectiveness of the proposed design methods. Moreover, it is suitable for practical application.

In this paper, we investigate the impulse effect in nonlinear singular system, since the existence of the nonlinear dynamics, we use the Differential Mean Value Theorem based method to transfer the nonlinear singular system into a linear parameter varying system. It should be noted that Differential Mean Value Theorem is an identical transmission, thus, for the nonlinear system, if we transfer the nonlinear system into a linear system via differential mean value theorem, the properties of the original system will not be changed. Based on this point, we try to analyze the transferred singular system by some existence method which applied to the linear singular system.

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.

This paper deals with the finite-time stability problem of non-linear singular multi-agent systems subject to controller gain disturbance via a distributed non-fragile controller. The existing literature on this problem only applies to normal multi-agent systems, or ignores the possible change of control gain in the practical application of the controller, or requires that there is no time-varying delay in the control input. How to tackle the finite-time stability problem of singular multi-agent systems by considering input time-varying delay, Lipschitz non-linear dynamics and controller gain perturbation simultaneously is an open issue. In order to solve this problem, a distributed non-fragile controller is proposed for each agent to make the finite-time stability problem solved for any connected undirected connection topology. With the help of a Linear matrix inequality and a Lyapunov integral appropriate expression, the difficulty caused by the irreversibility of singular system matrices is solved. Then, a sufficient condition to ensure the finite-time stability of the closed-loop system is obtained for the singular multi-agent system including controller disturbance, input–output delay and non-linear dynamics. Finally, two numerical examples are used to illustrate the effectiveness of the proposed method.