In this study, the author discusses a Pareto strategy implemented via state and static output feedback for a class of weakly coupled large-scale discrete-time stochastic systems with state- and control-dependent noise. The asymptotic structure along with the uniqueness and positive semi-definiteness of the solutions of cross-coupled non-linear matrix equations (CNMEs) is newly established via the implicit function theorem. The main contribution of this study is the proposal of a parameter-independent local state and static output feedback Pareto strategy. Moreover, a computational approach for solving the CNMEs is also considered if the information about the small parameter is available. Particularly, a new iterative algorithm based on the linear matrix inequality is established to design a Pareto strategy. Finally, in order to demonstrate the effectiveness of the proposed design method, a numerical example is provided for practical aircraft control problems.

The problem of designing H_∞ filters for delta operator formulated systems with low sensitivity to filter coefficient variations is investigated. The delta operator provides a theoretically unified formulation of continuous-time and discrete-time systems and also has the advantage of better numerical properties at high sampling rates. In addition to the standard H_∞ criterion, the H_∞ norm of the sensitivity function is introduced in order to improve the designed filter's insensitivity to the filter coefficient variations. Finsler's Lemma is used to derive novel sufficient conditions which are adapted to treat this multiplicative objective optimisation problem in a potentially less conservative framework. Linear matrix inequality conditions are obtained for the existence of admissible filters with respect to additive/multiplicative coefficient variations based on two different types of sensitivity measures. Finally, the effectiveness of the proposed method is illustrated by a numerical example. It is shown that the delta operator approach offers better coefficient sensitivity than the traditional shift operator approach when the sampling rate is high.

A consequent and consistent continuous-time approach to system parameter estimation is introduced. Estimation algorithms, the underlying quality criteria and models of identified systems are described in the continuous-time domain, while suitable discretising operations are performed solely for the purpose of ultimate numerical realisation of estimation procedures. The considered indices of estimation quality take the form of integrals of absolute prediction errors rather than a common form of integrals or sums of square errors. In order to overcome the problem of analytical minimisation of such non-differentiable criteria, an approximate method is derived and applied in practical implementation of the resultant estimation schemes. Specific weighting mechanisms utilised in the algorithms allow for tracking the time-variant parameters of non-stationary systems, while with the employed instrumental variable the accuracy of estimates gets improved by means of suppression of the asymptotic bias. Following the so-called direct approach, an auxiliary discrete-time model that retains ‘physical’ parameterisation is obtained based on ‘finite-horizon’ spline-based integration of both sides of the presumed differential equation. In this aspect, application of splines makes the respective discrete-time processing resistant to cumulation of numerical errors. The attached numerical examples demonstrate the performance of the discussed estimation routines.

This study presents an accurate and fast method for large-signal discrete-time simulation of current controlled DC/DC buck converter in continuous conduction mode. It employs modal decomposition of the state transition matrix for each topology, resulting in an exact and computationally efficient set of decoupled discrete-time state equations. This enables one to obtain an accurate solution for duty ratios iteratively, by equating the switching conditions of the state variables with state equations, which are non-linear in duty ratio. In the absence of a compensating ramp, an efficient way to compute duty ratios explicitly, without iteration, is also suggested. Subsequently, state variables are propagated through the ON and OFF periods, using the state equations exactly but without the need to compute a matrix exponential. This way numerical integration at multiple intermediate points between two switching instants of interest is avoided, which makes the simulation considerably faster, leading to significantly reduced storage requirement compared to common simulation methods, such as using SPICE. It is shown under different parametric conditions that the proposed method has superior accuracy over several approximate simulation methods proposed in the literature. The method can be generalised for other converter topologies, operational modes and control configurations with appropriate changes.

This study is concerned with the quantised stabilisation of linear discrete systems with packet dropout. Based on the zoom strategy and Lyapunov theory, for a given packet dropout rate, a sufficient condition is given for the closed-loop system to be mean square stable. A numerical simulation is presented to show the effectiveness of the main result.

The authors investigate in this study the problem of designing decentralised quantised ℋ_∞ feedback control for a class of linear interconnected discrete-time systems. The system has unknown-but-bounded couplings and interval delays. The quantiser has an arbitrary form that satisfies a quadratic inequality constraint. A linear matrix inequality (LMI)-based method using a decentralised quantised output-feedback controller is designed at the subsystem level to render the closed-loop system delay dependent asymptotically stable with guaranteed γ-level. To show the generality of the authors' approach, it is established that several cases of interest are readily derived as special cases. The authors illustrate the theoretical developments by numerical simulations.

In this study, a methodology to compute achievable performance bounds for non-right-invertible, stable, discrete-time MIMO systems is proposed. This methodology is based on the definition of a new performance index, which is the cumulative, squared and exponentially weighted tracking error to a step reference. The results include expressions for the optimal value of this performance index and for the Youla parameter that is able to achieve such performance. For a particular class of single-input multiple-output plants, closed-form expressions depending on the dynamic features of the plant are also obtained. A discussion on the selection of the speed of decay of the exponential weight and its influence on optimal closed-loop stability is included. Numerical examples are presented to illustrate the results.

In this study, the robust stochastic stability problem for discrete-time uncertain singular Markov jump systems with actuator saturation is considered. A sufficient condition that guarantees that the discrete-time singular Markov jump systems with actuator saturation is regular, causal and stochastically stable is established. With this condition, for full and partial knowledge of transition probabilities cases, the design of robust state feedback controller is developed based on linear matrix inequality (LMI) approach. A numerical example is given to illustrate the effectiveness of the proposed methods.