Input-to-state stability for discrete-time nonlinear switched singular systems

This correspondence paper is concerned with observer design problems for a class of unknown input switched descriptor systems under average dwell time switching signals. The switched descriptor system under consideration is first transformed into a general switched linear system, and then a switched reduced-order observer that can asymptotically estimate the system state without suffering the influence from the unknown inputs is developed. Besides, a high-order sliding mode observer is introduced to obtain the estimations of the output derivatives by using the system measured outputs. On the basis of estimations of the states and output derivatives, an unknown input reconstructing method is provided. Finally, two examples are presented to verify the effectiveness of the proposed approaches.

Observer Design and Unknown Input Reconstruction for a Class of Switched Descriptor Systems

The global stabilization design of a class of switched linear singular systems via a novel dwell-time switching is investigated and solved in this work. The distinguishing feature of the proposed method is that stability of all subsystems of the switched systems is not necessarily required. A time-varying coordinate transformation is introduced first in order to convert the problem into an equivalent one of reduced-order switched conventional linear system with state jumps. Then, by constructing certain new multiple time-varying Lyapunov functions, computable sufficient conditions for the global stabilization task are proposed within the framework of dwell-time switching. Given the assumed instability of individual subsystems, the stabilization of the switched system is achieved under the condition of confining the dwell time by a certain pair of upper and lower bounds, which restrict the growth of Lyapunov function for the actively operating subsystem, thus decrease the energy of the Lyapunov function of the overall switched system at switching times. In addition, the multiple time-varying Lyapunov functions method is also used to analyze the stability analysis of a class of switched linear singular systems with stable subsystems. Two illustrative examples are presented to demonstrate the effectiveness of the proposed method.

Dwell-time-based stabilization of switched linear singular systems with all unstable-mode subsystems

This paper is concerned with the input-to-state stabilization problem for a class of delayed differential systems. Both time-delay in state and bounded exogenous disturbances are taken into account in the model. An event-triggered strategy, which depends simultaneously on the latest sampled state and a non-negative threshold, is proposed to reduce the transmission frequency of the feedback control signals with guaranteed performance requirements. The notion of input-to-state practical stability is introduced to evaluate the dynamical performance of the controlled systems with considering the effects from both exogenous disturbances and event-triggered scheme. The estimations of the upper bounds for the system state and the measurement error are employed to analyze and further exclude the Zeno behavior for the proposed event-triggered scheme. The controller gain and the event-trigger parameters are co-designed in terms of the feasibility of certain matrix inequalities. A numerical simulation example is provided to illustrate the effectiveness of theoretical results.

Input-to-State Stabilization of Delayed Differential Systems With Exogenous Disturbances: The Event-Triggered Case

In this paper, mean square exponential input-to-state stability exp-ISS of stochastic memristive complex-valued neural networks SMCVNNs is investigated. By utilising Lyapunov functional and stochastic analysis theory, a sufficient criterion is derived to assure the mean square exp-ISS of the SMCVNNs. The obtained results not only generalise the previous works in the literature about real-valued neural networks as special cases, but also can be easily checked by parameters of system. Numerical simulations are given to show the effectiveness of our theoretical results.

Mean square exponential input-to-state stability of stochastic memristive complex-valued neural networks with time varying delay

This paper considers the problem of input-to-state stability for a class of nonlinear switched descriptor systems. According to the definition of input-to-state stability, sufficient conditions are derived to ensure that the system is input-to-state stable based on the dwell time approach and the Gronwall–Bellman inequality. Compared with existing methods, it is more convenient to design the controller for each subsystem, because it does not need to construct the input-to-state stable control Lyapunov function and design the specific structure of the control inputs. Finally, two numerical examples illustrate the feasibility and effectiveness of the proposed method.

Input-to-state stability analysis for a class of nonlinear switched descriptor systems

This article considers the issues of robust H∞ guaranteed cost control and memory state feedback stabilization for a class of uncertain switched descriptor delayed systems with nonlinear disturbance. Sufficient conditions for the existences of robust H∞ guaranteed cost controller in terms of linear matrix inequalities and switching strategy are proposed based on generalized Lyapunov function and convex optimization approach, and the memory state feedback controller ensures that the closed-loop systems satisfy the guaranteed cost function with a prescribed H∞γ-disturbance attenuation. Moreover, a convex optimization problem with linear matrix inequality constraints is formulated and solved by mean of the linear matrix inequality toolbox, and the optimal H∞ guaranteed cost memory state feedback controller with an upper bound of cost function is obtained. Finally, a numerical example illustrates the effectiveness of the proposed method.

Kun Yang

Papers

Input-to-state stability analysis for a class of nonlinear switched descriptor systems

Robust H∞ guaranteed cost control for uncertain switched descriptor delayed systems with nonlinear disturbance: