Constrained control of switched positive systems with discrete and distributed delays

This paper is concerned with constrained control of switched positive linear systems with discrete and distributed delays. Our goal is to design a nonnegative controller with a prescribed upper bound, such that the closed-loop system is positive and its state trajectory is located in a boundary whenever the initial condition is within the same boundary. In addition, we investigate the case when the state trajectory never reaches the boundary. It is shown that these problems are solvable via linear programming. Both continuous- and discrete-time cases are investigated in this paper. Finally, several illustrative examples are provided to show the validity of the proposed approach. © 2014 TCCT, CAA.postprin

Robust stability and stabilization of discrete singular systems: An equivalent characterization

This note deals with the problems of robust stability and stabilization for uncertain discrete-time singular systems. The parameter uncertainties are assumed to be time-invariant and norm-bounded appearing in both the state and input matrices. A new necessary and sufficient condition for a discrete-time singular system to be regular, causal and stable is proposed in terms of a strict linear matrix inequality (LMI). Based on this, the concepts of generalized quadratic stability and generalized quadratic stabilization for uncertain discrete-time singular systems are introduced. Necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are obtained in terms of a strict LMI and a set of matrix inequalities, respectively. With these conditions, the problems of robust stability and robust stabilization are solved. An explicit expression of a desired state feedback controller is also given, which involves no matrix decomposition. Finally, an illustrative example is provided to demonstrate the applicability of the proposed approach.published_or_final_versio

Time-Delay Systems

Time delay is very often encountered in various technical systems, such as electric, pneumatic and hydraulic networks, chemical processes, long transmission lines, robotics, etc. The existence of pure time lag, regardless if it is present in the control or/and the state, may cause undesirable system transient response, or even instability. Consequently, the problem of controllability, observability, robustness, optimization, adaptive control, pole placement and particularly stability and robustness stabilization for this class of systems, has been one of the main interests for many scientists and researchers during the last five decades

Continuous-Time Switched H∞ Proportional-Integral observer: Application for sideslip and road bank angles estimation

International audience— In this work, a Continuous-Time Switched H ∞ Proportional-Integral (CTSH ∞ PI) observer is presented. The estimation method is based on a proportional-integral observer introduced by [13], [11], [12]. The estimation method is used to estimate simultaneously the state variables and unknown inputs of switched systems. A design method is established using a common Lyapunov function and H ∞ norm. Its stability and global convergence conditions are proved and expressed in term of LMIs. All conditions are established under given switching signals. The estimation method is applied in vehicle dynamics to estimate simultaneously the vehicle sideslip angle and road bank angle. Moreover, the switching signal is deduced from measured premise variables. Simulation tests with experimental data are included to demonstrate the advantage of this method

Integral Sliding Mode Control for Markovian Jump T-S Fuzzy Descriptor Systems Based on the Super-Twisting Algorithm

This paper investigates integral sliding mode control problems for Markovian jump T-S fuzzy descriptor systems via the super-twisting algorithm. A new integral sliding surface which is continuous is constructed and an integral sliding mode control scheme based on a variable gain super-twisting algorithm is presented to guarantee the well-posedness of the state trajectories between two consecutive switchings. The stability of the sliding motion is analyzed by considering the descriptor redundancy and the properties of fuzzy membership functions. It is shown that the proposed variable gain super-twisting algorithm is an extension of the classical single-input case to the multi-input case. Finally, a bio-economic system is numerically simulated to verify the merits of the method proposed

Discrete Time Systems

Discrete-Time Systems comprehend an important and broad research field. The consolidation of digital-based computational means in the present, pushes a technological tool into the field with a tremendous impact in areas like Control, Signal Processing, Communications, System Modelling and related Applications. This book attempts to give a scope in the wide area of Discrete-Time Systems. Their contents are grouped conveniently in sections according to significant areas, namely Filtering, Fixed and Adaptive Control Systems, Stability Problems and Miscellaneous Applications. We think that the contribution of the book enlarges the field of the Discrete-Time Systems with signification in the present state-of-the-art. Despite the vertiginous advance in the field, we also believe that the topics described here allow us also to look through some main tendencies in the next years in the research area

Stability of Switched Linear Discrete-Time Descriptor Systems with Explicit Calculation of a Common Quadratic Lyapunov Sequence

Abstract-In this paper, the stability of a switched linear regular descriptor system is considered. It will be shown that if a certain simultaneous triangularization condition on the subsystems is fulfilled and all the subsystems are stable then the switched system is stable under arbitrary switching. The result involves different descriptor matrices and extends to the singular case well-known results from the standard one. Furthermore, an explicit construction of a common Lyapunov sequence for a set of discrete-time regular linear descriptor subsystems is performed. The main novelty of the proposed approach is that the common Lyapunov sequence can be easily computed in comparison with previous works which either presented computationally-demanding methods or did not construct the common Lyapunov sequence explicitly

Preview Tracking Control of Linear Periodic Switched Systems with Dwell Time

This paper studies the preview tracking control problem for linear discrete-time periodic switched systems. Firstly, an augmented error system is constructed for each subsystem by stabilizing the augmented error systems through the method of optimal preview control, and the tracking problem of the switched system is transformed into the switched stability problem of closed-loop augmented error systems. Secondly, a switched Lyapunov function method is applied to search the minimal dwell time satisfying the switched stability of the closed-loop augmented error systems. Thirdly, the switched preview control input is solved from the controller of the individual augmented error system, and then the sufficient conditions and the preview controller can be obtained to guarantee the solvability of the original periodic switched preview tracking problem. Finally, numerical simulations show the effectiveness of the stabilization design method