Stabilization of Discrete-Time Delayed Systems in Presence of Actuator Saturation Based on Wirtinger Inequality (original) (raw)
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This paper contemplates the H∞ control of discrete-time delayed systems together with actuator saturation, parametric uncertainties and disturbances. H∞-based state feedback controller is conceived to stabilise the closed loop system. Lyapunov Krasovskii functional (LKF), discrete Wirtinger-based summation inequality and convex hull approach are combined to obtain novel regional stability conditions. The estimated attraction domain is maximised using an optimisation method along with linear matrix inequality (LMI). A comparative study is shown between the obtained and existing findings. The results are found to be less conservative than the prior ones. Finally, instances signify efficacy of presented approaches.
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IEE Proceedings - Control Theory and Applications, 2002
The problem of delay-dependent stabilisation of linear continuous-time systems with time delay in the state, additive bounded disturbances and limited actuators is presented. A design procedure based on the solution of coupled matrix inequalities and the use of the S-procedure is proposed. The links and the trade-offs between tolerance to both disturbance and delay, and the size of the region inside which the stability of the closed-loop saturated system is assured are discussed.
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This paper deals with the problem of robust stabilization for uncertain systems with input saturation and time delay in the state. The parameter uncertainties are time-varying and unknown but are norm bounded. Sufficient conditions obtained via a linear matrix inequality formulation are stated to guarantee the local stabilization. The method of synthesis consists in determining simultaneously a state feedback control law and an associated domain of safe admissible states for which the stability of the closed-loop system is guaranteed when control saturations effectively occur. Numerical examples are used to demonstrate the effectiveness of the proposed design technique.
ISRN Applied Mathematics, Hindawi, 2014
The problem of global asymptotic stability of a class of uncertain discrete-time systems in the presence of saturation nonlinearities and interval-like time-varying delay in the state is considered. The uncertainties associated with the system parameters are assumed to be deterministic and normbounded. The objective of the paper is to propose stability criteria having considerably smaller numerical complexity. Two new delay-dependent stability criteria are derived by estimating the forward difference of the Lyapunov functional using the concept of reciprocal convexity and method of scale inequality, respectively. The presented criteria are compared with a previously reported criterion. A numerical example is provided to illustrate the effectiveness of the presented criteria.
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We address the problem of robust input-to-state stabilization of parameter-varying discrete-time systems with time-varying state delay, saturating actuators, and subject to ℓ2-limited disturbance. It is assumed that the delay belongs to a known interval and its maximum variation between two consecutive instants is taken into account. The proposed convex delay-dependent conditions for the synthesis of robust state feedback controllers ensure local input-to-state stability of the closed-loop system for a set of initial conditions and for energy bounded disturbance signals. However, the computed controllers do not require the real-time knowledge of the delay. The approach is based on the rewriting of the saturating and delayed system in terms of a switched uncertain augmented delay-free system with a dead-zone non-linearity and on the application of the generalized sector condition. To illustrate the efficiency of our approach, we compare it by means of numerical examples with others found in the literature.