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A new discrete time fault tolerant control system (DTFTCS) model is developed. The model represents a discrete version of fault tolerant control systems with Markovian parameters (FTCSMP). The proposed model is consistent with the general class of FTCSMP by defining two Markovian processes: one for fault detection and isolation (FDI) and the second represents the failures in control actuators. Stability...
A feedback linearization based direct adaptive neural control scheme is proposed for a class of affine nonlinear discrete time systems. Two radial basis function networks are used to approximate the unknown system dynamics. The weight update laws for the networks are derived to make the closed loop error dynamics Lyapunov stable. The proposed control scheme removes the need for any projection algorithm...
A bilinear DTFTCS model with static output feedback controller is developed. The model is corrupted by additive and multiplicative noises and disturbances. Second moment stability for the proposed bilinear DTFTCS is to be characterized. Necessary and sufficient stability conditions are derived in terms of nonlinear matrix inequalities. Given a set of control gains, sufficient conditions that test...
A discrete time fault tolerant control system (DTFTCS) with static output feedback controller is developed. The proposed model consider the case of DTFTCS with limited accessibility for system states. The stochastic behavior of the proposed DTFTCS is to be investigated for the case of actuating signal being feedback over noisy channels. Second moment stability is defined, and necessary and sufficient...
Testable second moment stability conditions for discrete-time supervisory control systems were recently developed using the Hybrid Jump Linear Systems (HJLSpsilas) framework. These tests are extended here to sampled-data supervisory control systems using the new sampled-data HJLS (SD-HJLS) framework. It is shown first that the p-moment stability of SD-HJLSpsilas equipped with ideal sample and hold...
An input-delayed DTFTCS model in noisy environments with state feedback controller is developed. Delay-independent results are obtained using Lyapunov function approach and formulated as feasibility solution for a set of linear matrix inequalities (LMI). For a given state feedback gains, testable trackable sufficient conditions that guarantee the second moment stability and achieve delta-level of...
This paper addresses stabilization problem with decay rate analysis for discrete-time linear systems subject to actuator saturation. The saturation-dependent Lyapunov function is exploited to propose new stability conditions by introducing additional slack variables. Especially, elimination Lemma is used to show the stable property of one slack variable. If the stable slack variable is specified a...
We consider the stabilization problem for networked control systems (NCSs) with uncertain, time-varying network-induced delays and a bounded number of subsequent packet dropouts. A discrete-time model, describing a NCS with packet dropouts and time-varying delays, that can be both smaller and larger than the sampling interval, is presented. Based on this NCS model sufficient LMI conditions are proposed...
This paper deals with achievable performance in the control of multivariable systems, with a particular degree of sparsity. The systems to be considered are linear, stable, time-invariant and discrete-time, and it is assumed that they can be reasonably described by a diagonal plus one interconnection structure. The performance loss when ignoring the off-diagonal term is quantified and also a comparison...
A problem of stabilization about uncertain networked control systems (NCSs) with random but bounded delays is discussed in this paper. By using augmented state-space method, this class of problem can be modeled as discrete-time jump linear system governed by a finite-state Markov chains. A new switched model based on probability is proposed to research problems of reliable control when actuators become...
In this paper, stochastic stability for discrete-time singular systems with Markov jump parameters is addressed. We present a set of coupled generalised Lyapunov equations (CGLEs) that serves as a necessary and sufficient condition for stochastic stability. A method for solving the obtained CGLEs is also presented, based on iterations of usual descriptor Lyapunov equations. An illustrative example...
In this paper we consider the finite-time stability problem for discrete-time linear systems. Differently from previous papers, the stability analysis is performed with the aid of polyhedral Lyapunov functions rather than using the classical quadratic Lyapunov functions. In this way we are able to deal with more realistic constraints on the state variables; indeed, in a way which is naturally compatible...
This paper presents a formal axiomization of the notion that (proof) complexity implies (property) fragility and illustrates this framework in the context of the stability of both discrete-time and continuous-time linear systems.
In the problem of input-to-state stabilization of nonlinear systems, synthesis of input-to-state stabilizing feedback laws is usually carried out off-line. This results in a constant input-to-state stability (ISS) gain, which is guaranteed for the closed-loop system. As an alternative, we propose a finite dimensional optimization problem that allows for the simultaneous on-line computation of an ISS...
This paper addresses stability analysis of sampled-data piecewise-affine (PWA) systems consisting of a continuous-time plant and a discrete-time emulation of a continuous-time state feedback controller. We consider the sampled-data system as a delayed system with a variable delay. The paper then presents conditions under which the trajectories of the sampled- data closed-loop system will converge...
Communication channels impose a number of obstacles to feedback control. One recent line of work considers the problem of feedback stabilisation subject to a constraint on the channel signal-to-noise ratio (SNR). It has been shown for continuous-time systems that the optimal control problem of achieving the infimal SNR can be formulated as a linear quadratic Gaussian (LQG) control problem with weights...
Motivated by the widespread use of networked and embedded control systems, an algorithm for stability analysis is proposed for sampled-data feedback control systems with uncertainly time-varying sampling intervals. The algorithm is based on the robustness of discrete-time systems against perturbation caused by the variation of sampling intervals. The validity of the algorithm is demonstrated by numerical...
The problem of Hinfin filtering for a class of discrete-time Markovian jump linear systems (MJLS) with partly unknown transition probabilities is investigated in the paper. The considered systems are more general, which cover the MJLS with completely known and completely unknown transition probabilities as two special cases. A mode-dependent full-order filter is constructed and the bounded real lemma...
A DTFTCS in noisy environments subject to delays and driven by a state feedback controller is developed. Second moment stability for the proposed delayed DTFTCS is investigated. A delay-independent sufficient condition that guarantee the Hinfin second moment stability and achieve delta- level of disturbance rejection is derived and proved. Results are obtained using Lyapunov function approach and...
The stochastic behavior of DTFTCS with norm bounded parameter uncertainties in noisy environments is studied. The uncertainties are assumed to be unknown but bounded. Second moment stability for the uncertain DTFTCS driven by a state feedback control law is to be investigated. Sufficient conditions that guarantee the second moment stability and achieve a minimum of delta-level of disturbance rejection...
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