Robust H∞ control of stochastic linear systems with input delay by predictor feedback

This note deals with the delay-dependent stability and stabilization of linear system with state and input delays. Firstly, for the nominal system, by introducing the augmented Lyapunov functional and some free-weighting matrices, new delay-dependent stability and stabilization criteria of the system are presented. Then, these new conditions are extended to handle norm-bounded uncertain systems with state and input delays, which show less conservativeness. Numerical examples are given to illustrate the effectiveness of the proposed results.

This article concerns the stability and stabilisation of a linear system with both state and input delays. First, the combination of an augmented Lyapunov functional and the free-weighting-matrix technique yields a new delay-independent stability criterion that includes the widely used one as a special case. This criterion is then extended to a new delay-dependent stability criterion by employing an integral inequality. Based on that, a stabilisation approach to design a state feedback controller is presented that requires no parameter tuning, as is needed with some existing methods. Finally, numerical examples illustrate that the method is effective and is an improvement over existing ones.

Stabilizability of Bimodal Piecewise Linear Systems With Continuous Vector Field

On the quasi-decentralized estimation and control of linear stochastic systems

First, a review of some recent developments in stochastic adaptive control of linear stochastic systems is given. By integrating and refining several basic ideas in these developments, a relatively complete asymptotic solution to the adaptive control problem is then provided for such systems. The solution involves parallel implementation of a few basic recursive identification algorithms that serve to complement each other. It also involves occasional use of a dither signal to probe the system for information.

This paper investigates the stabilization of large scale discrete-time linear control systems by observer-based reduced order controllers. Sufficient conditions are derived for the design of observer-based reduced order controllers for the large scale discrete-time linear control systems by obtaining a reduced order model of the original linear plant using the dominant state of the system. A separation principle has been established in this paper which shows that the observer poles and controller poles can be separated and hence the pole placement problem and observer design problem are independent of each other.KeywordsModel reductionreduced-order controllersstabilizationdominant stateobserversdiscrete-time linear systems

This paper addressed the problem of delay dependent stabilization for linear parameter-varying systems with time-varying state and input delays. A new delay-dependent criterion is developed by constructing the reduction method and combining with the parameter-dependent Lyapunov approach. Sufficient conditions are presented to design gain-scheduled controller to stabilize the closed-loop systems from past input information in terms of parameterized linear matrix inequalities. The effectiveness is shown via an numerical example.

BMI Approach to the Interconnected Stability and Cooperative Control of Linear Systems

The stabilization of dynamical systems with input delay using a generalized predictor feedback controller is investigated. With transforming the design procedure into the stabilization problem of a system controlled by a dynamic output feedback controller, predictor feedback gains are synthesized via linear matrix inequalities which are more flexible and extendable in comparison with the conventional predictor feedback method. Simulation examples demonstrate the effectiveness of the design method.

Predictor-based stabilisation results are provided for nonlinear systems with input delays and a compact absorbing set. The control scheme consists of an inter-sample predictor, a global observer, an approximate predictor, and a nominal controller for the delay-free case. The control scheme is applicable even to the case where the measurement is sampled and possibly delayed. The input and measurement delays can be arbitrarily large but both of them must be constant and accurately known. The closed-loop system is shown to have the properties of global asymptotic stability and exponential convergence in the disturbance-free case, robustness with respect to perturbations of the sampling schedule, and robustness with respect to measurement errors. In contrast to existing predictor feedback laws, the proposed control scheme utilises an approximate predictor of a dynamic type that is expressed by a system described by integral delay equations. Additional results are provided for systems that can be transformed to systems with a compact absorbing set by means of a preliminary predictor feedback.

Stabilization of linear systems with distributed input delay and input saturation

This article aims at proposing an adaptive neural control strategy for a class of nonlinear time-delay systems with input delays and unknown control directions. Different from previous researches that investigated delays and constraints separately, the novelty of this article lies in that it simultaneously considers delays (state and input delays) and input constraints (magnitude and rate constraints) for a class of uncertain nonlinear systems. In this article, the uncertain states and input delays are handled by integrating a constructed auxiliary system that functions as an observer with neural networks (NNs), with which the adverse effects caused by the uncertain states and input delays can be approximated and compensated. By involving smooth hyperbolic tangent functions in the designed auxiliary system, the problem of magnitude and rate constraints of the control input is fully addressed. Then, the backstepping technique runs through the entire control designing process, which allows the designed adaptive neural control strategy to handle the input constraints and delays at the same time. Furthermore, Nussbaum functions are employed to resolve the problem of unknown control directions. Due to the introduction of an input-driven filter, only the output of the system is required to be measured as the control feedback, which promotes the applicability of the designed controller. Under the proposed control scheme, semiglobal, uniform, and ultimate boundedness of all signals of the closed-loop system is realized with uncertain control directions, input and state delays, and guaranteed magnitude and rate constraints of control inputs. Finally, simulation results are illustrated to verify the effectiveness of the presented control method.

Constrained Stabilization of Multi-Input Linear Systems with Distinct Input Delays

This paper is concerned with stabilization of linear systems with arbitrarily large but bounded time-varying delay in the input. A pole assignment based low gain feedback design is adopted to solve the problem. Both delay-dependent and delay-independent results are presented and a series of sufficient conditions for guaranteeing the stability of the closed-loop system are established. By using properties of this class of low gain feedback laws and the properties of certain transcendental equations, distribution of the zeros of the closed-loop characteristic equation is described. As a result, a necessary and sufficient condition is identified that guarantees the stability of the closed-loop system. A numerical example is given to illustrate the effectiveness of the proposed approach.

The stabilization of nonlinear stochastic systems with input and output delays is investigated in this article. First, an observer that includes input delay information is designed to estimate the state information after eliminating the effect of input delay. Second, a predictive scheme with delay information is utilized to predict the system state affected by output delay, and an event‐triggered predictive controller is established to eliminate the effects of input and output delays simultaneously. Subsequently, the convergence of the prediction error is analyzed by utilizing a recursive method, and a sufficient condition to ensure the global exponential stability is given by constructing a new closed‐loop system. Finally, numerical simulations of two nonlinear stochastic systems with different delay sizes are utilized to verify the impact of the event‐triggered predictive control in addressing the stabilization of nonlinear stochastic systems with time delays.