State Saturation Nonlinearities Research Articles

Optimal guaranteed cost control of discrete-time uncertain systems subjected to state saturation nonlinearity

This paper investigates the optimal guaranteed cost (GC) control problem for uncertain discrete-time (DT) systems with state saturation nonlinearities via static-state feedback. The parameter uncertainties in the system state and input matrix are considered to be norm bounded. Utilizing Lyapunov theory and sector-based characterization of saturation nonlinearities, a novel criterion for the existence of GC controllers is proposed. The criterion is expressed in the framework of linear matrix inequalities (LMIs) and is thus computationally tractable. The proposed GC controllers make the closed-loop (CL) system asymptotically stable and ensure an adequate level of performance for all admissible parameter uncertainties. To design an optimum GC controller, a convex optimization problem with LMI constraints is formulated. The effectiveness of the proposed approach is illustrated by examples.

Resilient RMPC for Cyber-Physical Systems With Polytopic Uncertainties and State Saturation Under TOD Scheduling: An ADT Approach

This article presents a resilient robust model predictive control (RMPC) strategy for cyber-physical systems (CPSs) with polytopic uncertainties and state saturation nonlinearities under the try-once-discard (TOD) scheduling. To reduce the transmission burden, a so-called TOD protocol is adopted to schedule the nodes. The objective of the addressed problem is to design a set of resilient RMPC controllers such that, in the simultaneous presence of polytopic uncertainties and state saturations under the TOD protocol, the resilience, robustness, and exponential stability are guaranteed for the underlying CPSs. With the help of TOD-dependent Lyapunov-like function, and the average dwell-time (ADT) approach, sufficient conditions are obtained to guarantee the recursive feasibility of the proposed resilient RMPC approach and the exponential stability of the closed-loop system. Finally, two examples including a high-purity distillation process and a numerical simulation are used to demonstrate the effectiveness of the proposed methods.

Robust model predictive control for polytopic uncertain systems with state saturation nonlinearities under Round‐Robin protocol

SummaryThis paper is concerned with the robust model predictive control (RMPC) problem for polytopic uncertain systems with state saturation nonlinearities under the Round‐Robin (RR) protocol. With respect to the practical application, one of the most commonly encountered obstacles that stem from the physical limitation of system components, ie, state saturation, is adequately taken into consideration. In order to reduce the network transmission burden and improve the utilization of the network from the controller nodes to the actuator node, a so‐called RR protocol is employed to orchestrate the data transmission order. At each transmission instant, only one controller node that obtains the priority is accessible to the shared communication network. Our aim of the underlying problem is to design a set of controllers in the framework of RMPC such that the closed‐loop system is asymptotically stable. By taking the influence of the RR protocol and the state saturation precisely into account, some sufficient criteria are established in terms of the token‐dependent Lyapunov‐like approach. Then, an online optimization problem subjected to some matrix inequality constraints is provided, and the desired controllers can be obtained by solving the certain upper bound of the objective addressed. Finally, a distillation process example is provided to illustrate the effectiveness of the proposed RMPC approach.

Study and Application of State Estimator for Time-Delay Systems with State Saturation Nonlinearities

The design and application of state estimator for a class of time-delay systems with state saturation nonlinearities are firstly explored. Based on the Lyapunov-Razumikhin functions, delay-dependent sufficient conditions are established to guarantee the asymptotic stability of the error between the state estimate and the true state. Besides, an upper bound of arbitrary time-varying delays is derived to assure that the resulting error can converge asymptotically to zero. Finally, applications to the secure communication and simulation results are given to demonstrate the feasibility and effectiveness of the main results.

Comment on ‘Stability analysis and controller synthesis for discrete linear time-delay systems with state saturation nonlinearities’

A recently reported paper (Ji, X., Liu, T., Sun, Y., and Su, H. (2011), ‘Stability analysis and controller synthesis for discrete linear time-delay systems with state saturation nonlinearities’, International Journal of Systems Science, 42, 397–406) for the global asymptotic stability analysis and controller synthesis for a class of discrete linear time delay systems employing state saturation nonlinearities is reviewed. It is claimed in Ji, Liu, Sun and Su (2011) that a previous approach by Kandanvli and Kar (Kandanvli, V.K.R and Kar, H. (2009), ‘Robust stability of discrete-time state-delayed systems with saturation nonlinearities: Linear matrix inequality approach’, Signal Processing, 89, 161–173) is recovered from their approach as a special case. It is shown that this claim is not justified.

A new stability analysis and controller design method for discrete-time linear systems with saturation nonlinearities

The problems of stability analysis and controllers design for discrete-time linear systems subject to state saturation nonlinearities are investigated in this paper. Both full state saturation and partial state saturation are considered. It is well known to all that the controller design problem under state saturation is very difficult and complex to deal with. In order to overcome the difficulty, a new and tractable system is constructed, and it can be proved that the constructed system is with the same domain of attraction as the original system. With the aid of this property, to estimate the domain of attraction of the original system, an LMI-based method is presented for estimating the domain of attraction of the origin for the new constructed system under state saturation. Further, two optimization algorithms are developed for constructing dynamic output-feedback controllers and state feedback controllers, respectively, which guarantee that the domain of attraction of the origin for the closed-loop system is as ‘large’ as possible. An example is provided to demonstrate the effectiveness of the new method.

Stability analysis and controller synthesis for discrete linear time-delay systems with state saturation nonlinearities

The problem of global asymptotic stability analysis and controller synthesis for a class of discrete linear time-delay systems with state saturation nonlinearities is investigated. With the introduction of a free matrix whose infinity norm is less than or equal to 1, the state of discrete linear time-delay systems with state saturation is bounded by a convex hull, which makes it feasible to apply a suitable Lyapunov functional to obtain a sufficient condition for global asymptotic stability. It is also shown that this condition can be extended to controller synthesis and discrete time-delay systems with partial state saturation. The obtained results are expressed in terms of matrix inequalities that can be solved by the presented iterative linear matrix inequality approach. The effectiveness of these results is demonstrated by some numerical examples.

H∞ control for linear systems with state saturation nonlinearities

AbstractThe problem of H∞ control for a class of linear systems with state saturation nonlinearities is considered in this paper. By introducing a row diagonally dominant matrix with negative diagonal elements and a diagonal matrix with positive elements, the H∞ control problem is reduced to a matrix inequality feasibility problem that can be solved by the proposed iterative linear matrix inequality algorithm. The effectiveness of the presented method is demonstrated by a numerical example. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

On global asymptotic stability of 2-D discrete systems with state saturation

A criterion for the global asymptotic stability of 2-D discrete systems described by the Roesser model employing state saturation nonlinearities is presented. The criterion is a less restrictive version of an earlier criterion due to Liu and Michel.

Interval criterion for stability analysis of discrete-time nonlinear systems with partial state saturation nonlinearities

A generalization of sufficient conditions for global asymptotic stability of the equilibrium of discrete-time nonlinear systems with saturation non linearity's on part of the states in the case of interval uncertainties is considered. When using quadratic form Lyapunov functions, sufficient conditions based on the positive definite interval matrices are presented. In order to check this, a recently proposed method for determining the outer bounds of eigenvalues ranges is used. A numerical example illustrating the applicability of the method suggested is solved in the end of the paper.

Stability analysis of discrete-time systems in a state-space realisation with state saturation nonlinearities: linear matrix inequality approach

A computationally efficient linear matrix inequality (LMI)-based criterion for the global asymptotic stability of discrete-time systems in a state-space realisation with state saturation nonlinearities is presented. The criterion turns out to be an improved generalised version of a previously reported LMI-based criterion. The extension of the approach to a situation involving partial state saturation nonlinearities is performed.

Stability analysis of discrete-time systems in a state-space realisation with partial state saturation nonlinearities

A criterion for the global asymptotic stability of discrete-time systems in a state-space realisation with partial state saturation nonlinearities is presented. The criterion is compared with a previously reported criterion.

Stability analysis of continuous time planar systems with state saturation nonlinearity

This work establishes easy-to-verify necessary and sufficient conditions for global asymptotic stability of a class of continuous time planar systems which are subject to state saturation nonlinearities on both its state variables.

Stability analysis of systems with partial state saturation nonlinearities

Sufficient conditions for the global asymptotic stability of the equilibrium x/sub e/=0 of discrete-time dynamical systems which have saturation nonlinearities on part of the states are established. We utilize a class of positive definite and radially unbounded Lyapunov functions in establishing our results. When using quadratic form Lyapunov functions, our results involve necessary and sufficient conditions under which positive definite matrices can be used to generate Lyapunov functions for the systems considered herein.

Stability analysis of a class of systems with parameter uncertainties and with state saturation nonlinearities

AbstractFor linear systems with parameter uncertainties and subject to state saturation, we establish results concerning the global asymptotic stability of an equilibrium. In addition to providing a means for a qualitative analysis, these results also enable us to address the stabilizability of such systems by means of linear state feedback.Systems of the type considered herein capture two important phenomena commonly encountered in the modelling process: (i) system parameter uncertainties (which in the present case are modelled by means of interval matrices), and (ii) operation of systems over a wide range (which in the present case is accounted for by state saturation nonlinearities).We demonstrate the applicability of the present results by means of several specific examples.