Robust invariant control synthesis for discrete-time polytopic uncertain linear hybrid systems

This study is concerned with the problem of robust H 2 and H ∞ filtering for uncertain discrete-time linear systems. Two types of time-invariant parametric uncertainty, namely polytopic and ellipsoidal, are considered and represented by a linear fractional transformation structure. Obtained auxiliary variables by a convex optimisation problem, play the role of decoupling the Lyapunov variables and the robust filter parameters, in order to cast the problem into a linear matrix inequality-based optimisation problem. The design conditions are derived based on the quadratic separation concept and employing appropriate parameterisations for the corresponding set of multipliers. The merit of the methods presented in this study lies in their less conservatism than the existing methods for the polytopic uncertain systems, as well as presenting a new convex optimisation procedure for the robust filtering for the ellipsoidal uncertain systems.

This paper studies the design of uncertain linear discrete-time Networked Control Systems over imperfect communication channels with time-varying data loss. This leakage is modeled as stochastic parameter and norm-bounded uncertainties. In addition, this paper defines the necessary conditions for the design of the dynamic output feedback controller; subsequently, an iterative LMI approach is specified to compute the controller state parameters. The simulation results show that the designed controller improves the H∞ disturbance attenuation performance of the concerned uncertain system.

An adaptive control framework for stabilization of 1-dimensional linear uncertain discrete-time dynamical systems with symbolic feedback is developed. The plant output is assumed to be quantized and only its symbolic quantity is fed back to the controller. In the case of multi-dimensional systems, ideal system matrix is constructed so that the approach for the scalar systems can be applied in separate subspaces in the state space.

This paper considers a subclass of hybrid systems, which is the discrete-time linear switching systems whose changes in the dynamics are determined by exogenous, uncontrollable events, and resets are present. In the presence of uncertain parameter and non-symmetrical constrained control, based on the results of nominal linear switching systems, a necessary and sufficient condition to test the robustness of a state feedback controller is given. The candidate state feedback controller for this test is that stabilizing nominal discrete-time linear switching systems. Also, the method in this paper can be extended to the case which has state constraints. At last, a numerical example is presented to illustrate the technique.

Robust H∞ control for uncertain discrete-time state-delayed linear systems with markovian jumping parameters

H∞ control of discrete-time uncertain linear systems with quantized feedback

This paper is concerned with the robustness and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control problem of observer-based control for a class of uncertain linear discrete-time systems with both state and input delays. Under no disturbance input, the asymptotic stabilization for uncertain time-delay systems will be guaranteed. Linear Matrix Inequality(LMI) optimization approach is used to design the observer-based H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control. An example illustrates the application of the proposed technique.

The authors present a sufficient condition for quadratic stabilizability of uncertain linear discrete time systems using LQ (linear quadratic) regulators. The true system is represented by a nominal model plus additive terms representing the uncertainties in the state and input matrices. With a proper choice of these terms, one may represent the most common types of uncertainties encountered in the literature. The main result of the present work is a robustification procedure for discrete time LQ regulators, which is based on a sufficient condition for quadratic stabilizability. The conservativeness of the proposed condition is discussed and some examples are given. >

Backward reachability analysis is essential to synthesizing controllers that ensure the correctness of closed-loop systems. This article is concerned with developing scalable algorithms that underapproximate the backward reachable sets, for discrete-time uncertain linear and nonlinear systems. Our algorithm sequentially linearizes the dynamics and uses constrained zonotopes for set representation and computation. The main technical ingredient of our algorithm is an efficient way to underapproximate the Minkowski difference between a constrained zonotopic minuend and a zonotopic subtrahend, which consists of all possible values of the uncertainties and the linearization error. This Minkowski difference needs to be represented as a constrained zonotope to enable subsequent computation, but, as we show, it is impossible to find a polynomial-size representation for it in polynomial time. Our algorithm finds a polynomial-size underapproximation in polynomial time. We further analyze the conservatism of this underapproximation technique and show that it is exact under some conditions. Based on the developed Minkowski difference technique, we detail two backward reachable set computation algorithms to control the linearization error and incorporate nonconvex state constraints. Several examples illustrate the effectiveness of our algorithms.

One of the great challenges to control theory is to design controllers for the increasing size of uncertain large-scale systems. Such problems arise in many real-word applications and the systems are too large and too complex to be centralised controlled. For these reasons, the complex system is split into several interconnected subsystems and it is controlled in a decentralized fashion. In this article, a novel, original approach to the control of large-scale uncertain linear discrete-time systems by a decentralised controller is presented. In the existing references, such systems are divided into two groups: complex systems with strong or weak interactions. However, the new proposed approach depends on whether the system is stable or not. The design procedure consists of two steps: In the first step, the dynamic properties of the closed-loop decentralised controlled subsystems are determined in such a way that the stability, robustness, and performance of the closed-loop subsystems and the entire system are guaranteed. In the second step, a decentralised control algorithm must be designed that ensures the required properties of the subsystems that have been obtained in the first step. The advantage of this approach is that the decentralized controller design is performed on the subsystem level.

In this paper, the Bellman equation is used to solve the optimal adaptive control of quantized linear discrete-time system with unknown dynamics. To mitigate the effect of the quantization errors, the dynamics of the quantization error bound and an update law for tuning the range of the dynamic quantizer are derived. Subsequently, by using adaptive dynamic programming technique, the infinite horizon optimal regulation problem of the uncertain quantized linear discrete-time system is solved in a forward-in-time manner without using value and/or policy iterations. The asymptotic stability of the closed-loop system is verified by standard Lyapunov stability approach in the presence of state and input quantizers. The effectiveness of the proposed method is verified via simulation.

The problem of finite frequency (FF) H∞ full-order filtering design for discrete-time linear systems, with polytopic uncertainties, is investigated in this paper. Based on the generalized Kalman-Yakubovich-Popov (GKYP) lemma and a parameter dependent Lyapunov function, a set of sufficient conditions for the existence of the H∞ filter are established in terms of matrix inequalities, ensuring that the filtering error system is stable and the H∞ attenuation level from disturbance to the estimation error is minimized in the FF domain of the external disturbances. Then, in order to linearize and relax the obtained matrix inequalities, we apply Finsler's lemma twice, which provides extra degrees of freedom in optimizing the guaranteed H∞ performance, and we show how we can calculate the filter gain matrices by using these conditions. Numerical example is given to illustrate the effectiveness and the less conservatism of the proposed approach in comparison with the existing methods.

Discrete-time systems in state space subject to uncertainties in the state and input matrices as well as to finite-energy additive disturbances are considered. No statistical assumptions nor matching conditions are required. Necessary and sufficient conditions for quadratic stability by linear state feedback and output-disturbance attenuation below a prescribed value are derived independently of the uncertainty structure. These conditions are then applied to the case of convex polyhedral uncertainly and the robust synthesis problem is cast into a mathematical programming problem. Additional constraints like robust pole assignment in subregions of the complex plane can easily be fit into the design procedure. Numerical examples are provided.

This paper investigates a class of uncertain linear discrete-time systems subject to input rate saturation. A predictive sliding mode control approach is proposed which guarantees the control inputs remain bounded in the input rate saturation. Furthermore, the disturbance observer is developed to compensate for the system uncertainty and disturbance. Finally, the simulations demonstrate the effectiveness of the proposed predictive sliding mode control scheme.

This article is concerned with robust stability of uncertain discrete-time linear systems. The matrix defining the linear system (system matrix) is assumed to depend affinely on a set of time-invariant unknown parameters lying on a known polytope. Robust stability is investigated by checking whether a certain integer power κ of the uncertain system matrix has spectral norm less than one. This peculiar stability test is shown to be equivalent to the positivity analysis of a homogeneous symmetric matrix polynomial with precisely known coefficients and degree indexed by κ. A unique feature is that no extra variables need to be added to the problems being solved. Numerical experiments reveal that the value of κ needed to test robust stability is mostly independent of the system dimension but grows sharply as the eigenvalues of the uncertain system approach the unit circle. By identifying the proposed stability test with a particular choice of a parameter-dependent Lyapunov function, extra variables can be introduced, yielding linear matrix inequalities optimisation problems of improved convergence.