Output feedback stabilization of nonlinear networked control systems with non‐decreasing nonlinearities: a matrix inequalities approach

Output feedback stabilization of nonlinear dual-rate sampled-data systems via an approximate discrete-time model

This paper is concerned with fuzzy-model based stabilization of nonlinear networked control systems (NCSs) with time-varying transmission delays and transmission intervals based on a random-delay approach. The real-time distribution of input delays resulting from transmission delays and intervals is modeled as a dependent and nonidentically distributed process. Then a randomly switched Takagi-Sugeno fuzzy system with multiple input-delay subsystems is proposed to model the nonlinear NCSs. Based on an improved Lyapunov-Krasovskii method, which takes into account the real-time distribution of input delays in estimating cross-product integral terms, new sufficient conditions are deriveed for the exponential stability of the overall systems. The resulting controller design method is equivalent to a nonlinear convex optimization problem with LMI constraints. Numerical examples are presented to substantiate the effectiveness of our results.

Design of output feedback semiglobally practically input-to-state (SPIS) stabilizing controllers for nonlinear strict-feedback networked systems is considered. We first design continuous-time state feedback globally asymptotically (GA) stabilizing controllers and discrete-time reduced-order observers and combine the emulation of state feedback controllers and the designed observers to construct discrete-time output feedback controllers. Then we show that the designed controllers SPIS stabilize nonlinear strict-feedback networked control systems when transmission intervals are sufficiently small and communication networks satisfy suitable assumptions. A numerical example is also given to illustrate the efficiency of proposed design of controllers.

State estimation and stabilization for nonlinear networked control systems with limited capacity channel

The problem of local stabilization of nonlinear control systems with linearizations that contain uncontrollable modes on the imaginary axis is considered. A methodology of designing a stabilizing control is investigated. It involves the following steps: (1) reduction of the stability problem to the stability of the center manifold system, (2) simplification of the vector field on the center manifold using the theory of normal forms, and (3) finding conditions under which the simplified vector field is asymptotically stable. Three cases of degeneracies in the linearized system are treated, and sufficient conditions for the existence of stabilizing controls are given in each case. A theorem is presented regarding the robustness of the above control strategies. >

This chapter investigates the problem of stabilization of nonlinear discrete-time networked control systems (NCS) with event-triggering communication scheme in the presence of signal transmission delay. A Takagi–Sugeno (T–S) fuzzy model and parallel-distributed compensation (PDC) scheme are first employed to design a nonlinear fuzzy event-triggered controller for the stabilization of nonlinear discrete-time NCS. The idea of the event-triggering communication scheme (a soft computation algorithm) under consideration is that the current sensor data is transmitted only when the current sensor data and the previously transmitted one satisfy a certain state-dependent trigger condition. By taking the signal transmission delay into consideration and using delay system approach, a T–S fuzzy delay system model is established to describe the nonlinear discrete-time NCSs with event-triggering communication scheme. Attention is focused on the design of fuzzy event-triggered controller which ensures asymptotic stability of the closed-loop fuzzy systems. Linear matrix inequality- (LMI-) based conditions are formulated for the existence of admissible fuzzy event-triggered controller. If these conditions are feasible, a desired fuzzy event-triggered controller can be readily constructed. A nonlinear mass-spring-damper mechanical system is presented to demonstrate the effectiveness of the proposed method.

The stabilization of two-dimensional non-linear control systems is treated, although the main technique is applicable to more general systems. It combines the theory of centre manifolds and singularities of algebraic functions to design continuous, but not necessarily Lipschitz, stabilizing feedback control laws. In particular, the devices known as the Newton diagram and the Newton or Puiseux polygon are employed to construct uniformizing transformations. Finally, remarks are made about systems for which no continuous stabilizing feedback control law exists.

Fundamentals of the theory of non-linear pluse control systems

In this paper, the robust stabilization problem of uncertain networked control systems subject to packet dropouts and signal quantization. Random data packet dropouts in the channels are modeled as independent Bernoulli processes. Quantized signal measurement is handled by a sector-bound method, in which the quantization error is treated as sector-bounded uncertainty. Based on Lyapunov theory, a static feedback controller is obtained in terms of linear matrix inequality (LMI) to ensure the asymptotically stability of the closed-loop system. At last, a numerical simulation example is used to show the validity of the designed controller.

This article addresses the robust stability for a class of nonlinear uncertain discrete-time systems with convex polytopic of uncertainties. The system to be considered is subject to both interval time-varying delays and convex polytopic-type uncertainties. Based on the augmented parameter-dependent Lyapunov-Krasovskii functional, new delay-dependent conditions for the robust stability are established in terms of linear matrix inequalities. An application to robust stabilization of nonlinear uncertain discrete-time control systems is given. Numerical examples are included to illustrate the effectiveness of our results. MSC:15A09, 52A10, 74M05, 93D05.

Stability and H-infinity optimal control of nonlinear networked control systems (NNCSs) with distributed delays and disturbance are studied in this paper. We develop a hybrid Takagi-Sugeno fuzzy model for nonlinear plant interconnected with continuously dynamic output feedback controller. Sufficient conditions are derived by constructing Lyapunov-krasovskii functional, which insure that the system is asymptotically stable and could achieve γ - suboptimal H-infinity stabilization. Approach to obtaining disturbance attenuation level and parameters of sub-/optimal controller is given in the form of linear matrix inequalities.

We study the problem of output feedback stabilization for stochastic nonlinear systems. We consider a class of stochastic nonlinear systems in observer canonical form with stable zero-dynamics. We introduce a sequence of state transformations that transform the system into a lower triangular structure that is amenable for integrator backstepping design. Then we design the output feedback controller and prove that the closed-loop system is bounded in probability. Under an infinite-horizon risk-neutral cost criterion, the controller designed can guarantee an arbitrarily small long term average cost. Furthermore, when the disturbance vector field vanishes at the origin, the closed-loop system is asymptotically stable in the large, and the risk-neutral cost is guaranteed to be zero. With special care, the controller preserves the equilibrium of the nonlinear system.

Practical Stabilization of Nonlinear Control Systems

International audience

We study emulation-based stabilisation of nonlinear networked control systems communicating over multiple wireless channels subject to packet loss. Specifically, we establish sufficient conditions on the rate of transmission that guarantee ℒ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> stability-in-expectation of the overall closed-loop system. These conditions depend on the cumulative dropout probability of the network nodes for static protocols. We use the obtained stability results to study power control, where we show there are interesting trade-offs between the transmission rate, transmit power, and stability. Lastly, numerical examples are presented to illustrate our results.