Analysis Of Linear Systems Research Articles

Parametrised auxiliary function-based integral inequality for time delay system

ABSTRACT This paper employs two scalar parameters to extend auxiliary function-based integral inequality into a new formulations, say a parametrised auxiliary function-based integral inequality. Using these formulations, the constituent signals are utilised more efficiently by exploiting the interaction between them to reduce conservatism. Numerical example for stability analysis of linear systems with time-varying delay shows the improved performance of the proposed new formulations in terms of maximum delay bounds and decision variables.

Stability analysis and control synthesis of hybrid time-varying linear systems using a discretization-based approach

A strategy for stability analysis and control design concerning a class of hybrid linear time-varying (LTV) systems is proposed in this paper. First, the transition matrix of the system is computed and then used to formulate the stability analysis condition, unifying both the flows and jumps into a single continuous-time framework and resulting in a straightforward methodology for hybrid dynamics. Such condition is then adapted to yield the proposed synthesis techniques, capable of generating a time-varying state-feedback gain to stabilize the hybrid LTV system. A discretization procedure is then proposed for both analysis and synthesis conditions, resulting on a numerically suitable approach that allows the adaptation of any LTV discrete-time synthesis technique to deal with the considered hybrid LTV systems. Finally, to highlight the possibilities of the methodology, the conditions are adapted for the stabilization of sampled-data time-varying systems. Numerical examples illustrate the validity and potentialities of the proposed techniques.

Covariance-analytic performance criteria, Hardy-Schatten norms and Wick-like ordering of cascaded systems

This paper is concerned with robust performance analysis of linear stochastic systems acting as an integral operator on a standard Wiener process at the input and producing a stationary Gaussian random process at the output. We propose a performance criterion which uses the trace of an analytic function of the spectral density of the output process. This class of “covariance-analytic” cost functionals includes the usual mean square and risk-sensitive criteria as particular cases. Due to the “cost-shaping” analytic function, the covariance-analytic performance criterion depends on higher-order Hardy-Schatten norms of the system transfer function. We discuss the links of these norms with the asymptotic behaviour of cumulants of finite-horizon quadratic functionals of the system output and their variational properties pertaining to system robustness to statistically uncertain inputs which differ from the standard Wiener process. In the case of strictly proper finite-dimensional systems, governed in state space by linear stochastic differential equations, we develop a method for recursively computing the Hardy-Schatten norms through a recently proposed technique of rearranging cascaded linear systems, which resembles the Wick ordering of mixed products of noncommuting annihilation and creation operators in quantum mechanics. This computational procedure, which is one of the main results of the paper, involves a recurrence sequence of solutions to algebraic Lyapunov equations and represents the covariance-analytic cost as the squared H2-norm of an auxiliary cascaded system. These results are also compared with an alternative approach, which uses higher-order derivatives of stabilising solutions of parameter-dependent algebraic Riccati equations, and illustrated by a numerical example.

Stability Analysis of Linear Control Systems by Wall’s Continued Fraction Expansion

Stability Analysis of Linear Control Systems by Wall’s Continued Fraction Expansion

On a new approach of enriched operators

We establish the existence and uniqueness of fixed points of generalized contractions in the setting of Banach spaces and prove the convergence of Mann iteration for this general class of mappings. Also, we show the existence of fixed points and the convergence of Mann iteration as well for generalized nonexpansive mappings. Last but not least, we provide two applications, one from the field of numerical analysis of linear systems and another one dealing with functional equations. This new approach significantly extends the classes of enriched contractions and enriched nonexpansive mappings, and allows the use of Mann iteration as opposed to all papers on the subject, which necessarily have to rely on Krasnoselskij iteration.

Stability analysis of linear delayed systems based on an allowable delay set partitioning approach

This note is concerned with the stability analysis of linear systems with a time-varying delay, where the delay is assumed to be a periodically varying bounded function with restricted derivatives. Combining the allowable delay set (ADS) definition and the region partitioning technique, an ADS partitioning approach is proposed, and then by with aid of this approach, a novel Lyapunov–Krasovskii functional (LKF), namely delay-set-partition-based (DSPB) LKF, is developed. Compared with the previous LKF method, the main advantage of the DSPB LKF lies in allowing the considered system to construct its own LKF in each sub-ADS. By utilizing the proposed LKF, less conservative stability criteria are derived. Finally, two simulation examples are provided to verify the effectiveness and superiority of the proposed method.

A Behavioral Approach to Data-Driven Control With Noisy Input–Output Data

This paper deals with data-driven stability analysis and feedback stabilization of linear input-output systems in auto-regressive (AR) form. We assume that noisy input-output data on a finite time-interval have been obtained from some unknown AR system. Data-based tests are then developed to analyse whether the unknown system is stable, or to verify whether a stabilizing dynamic feedback controller exists. If so, stabilizing controllers are computed using the data. In order to do this, we employ the behavioral approach to systems and control, meaning a departure from existing methods in data driven control. Our results heavily rely on a characterization of asymptotic stability of systems in AR form using the notion of quadratic difference form (QDF) as a natural framework for Lyapunov functions of autonomous AR systems. We introduce the concepts of informative data for quadratic stability and quadratic stabilization in the context of input-output AR systems and establish necessary and sufficient conditions for these properties to hold. In addition, this paper will build on results on quadratic matrix inequalities (QMIs) and a matrix version of Yakubovich's S-lemma.

On the [formula omitted]-exponential stability of linear positive singular systems with multiple time-varying delays

This paper deals with α-exponential stability analysis of the continuous-time linear positive singular systems with multiple time-varying delays. First, α-exponential stability problem of the single delay case is addressed. For this purpose, delay-range dependent sufficient conditions for such systems, which are regular and impulse-free, are stated in the paper. Then, α-exponential stability conditions for systems with multiple constant delays are addressed, and after that, we extend our idea for stability to multiple delays. To show the usefulness of the proposed conditions, two numerical and practical examples are given.

Analysis of linear continuous-time systems by the use of the conformable fractional calculus and Caputo

Analysis of linear continuous-time systems by the use of the conformable fractional calculus and Caputo

A New Approach to the Energy-to-Peak Performance Analysis of Continuous-Time Markov Jump Linear Systems

A New Approach to the Energy-to-Peak Performance Analysis of Continuous-Time Markov Jump Linear Systems

Stability Analysis of Hybrid Integrator-Gain Systems using Linear Programming

Stability and performance of hybrid integrator-gain systems (HIGS) are mostly analyzed using linear matrix inequalities (LMIs) to construct continuous piecewise quadratic (CPQ) Lyapunov functions. To create additional methods for the analysis of HIGS and other conewise linear systems, a method based on linear programming (LP) for constructing continuous piecewise affine (CPA) Lyapunov functions is investigated. In this paper, it is shown how linear programming can be used to prove input-to-state stability and calculate upper bounds on the L1-gain and H1-norm. The numerical efficiency of this CPA (LP) method will be compared to that of the CPQ (LMI) method on a numerical example involving HIGS.

Stability Analysis and Stabilization of Semi-Markov Jump Linear Systems With Improved Efficiency of Probabilistic Information Utilization

Stability Analysis and Stabilization of Semi-Markov Jump Linear Systems With Improved Efficiency of Probabilistic Information Utilization

Modernization of ventilation systems for industrial premises

The article provides a theoretical justification for the possibility of modernizing the ventilation system of a production facility. The relevance of the study is dictated by the need to increase the efficiency of the ventilation system of a production facility through resource conservation and reduction of energy costs. Based on the analysis of the functioning ventilation system, the authors developed an engineering solution consisting of installing functional elements and changing the structure of the system. Modeling of the technical system and its verification were carried out using methods of analysis of linear dynamic systems in the SimInTech software environment. Determining the main parameters for optimizing a technical system and applying stochastic methods to analyze a database of daily temperature values made it possible to form an area of optimal functioning. All studies were carried out on the basis of the Institute of Risk Management and Integrated Safety of the Orenburg State Agrarian University, and the production base for the experimental studies was the research and production enterprise "PnevMax", which is developing a project for modernizing the ventilation system for the production premises of Stroilandiya LLC (Orenburg). Production tests of the modernized ventilation system for the operating premises showed an increase in the efficiency of use of production resources and a significant reduction in energy costs.

Stability of conformable fractional time-varying linear systems

In this paper, we investigate the exponential and asymptotic stability analysis of conformable fractional linear time-varying systems. We propose sufficient conditions for testing the asymptotic and exponential stability of conformable differential systems by using the notion of stable functions and differential Lyapunov inequalities. Furthermore, we apply the developed approach to the problem of conformable stabilisation and observer design for conformable fractional linear time-varying systems.

Equilibrium controllability analysis and input design of linear systems

Equilibrium controllability analysis and input design of linear systems

Stability analysis of linear systems with time-varying delay via some novel techniques

This paper concentrates on the stability analysis of linear systems with a time-varying delay. Firstly, a new Lyapunov–Krasovskii functional (LKF) is given, which involves more time delay cross-terms information. Secondly, an improved reciprocally convex inequality with higher estimation accuracy is derived. Then, on the basis of the constructed LKF and the improved reciprocally convex inequality, some new stability criteria with less conservative are proposed. Finally, the superiority of the obtained stability criteria is explained by two numerical examples.

Pattern evolution and modal decomposition of Faraday waves in a brimful cylinder

This paper investigates the steady-state pattern evolution of symmetric Faraday waves excited in a brimful cylindrical container when driving parameters much exceed critical thresholds. In such liquid systems, parametric surface responses are typically considered as the resonant superposition of unstable standing waves. A modified free-surface synthetic Schlieren method is employed to obtain full three-dimensional spatial reconstructions of instantaneous surface patterns. Multi-azimuth structures and localized travelling waves during the small-elevation phases of the oscillation cycle give rise to modal decomposition in the form of $\nu$ -basis modes. Two-step surface-fitting results provide insight into the spatiotemporal characteristics of dominant wave components and corresponding harmonics in the experimental observations. Arithmetic combination of modal indices and uniform frequency distributions reveal the nonlinear mechanisms behind pattern formation and the primary pathways of energy transfer. Taking the hypothetical surface manifestation of multiple azimuths as the modal solutions, a linear stability analysis of the inviscid system is utilised to calculate fundamental resonance tongues (FRTs) with non-overlapping bottoms, which correspond to subharmonic or harmonic $\nu$ -basis modes induced by surface instability at the air–liquid interface. Close relationships between experimental observations and corresponding FRTs provide qualitative verification of dominant modes identified using surface-fitting results. This supports the validity and rationality of the applied $\nu$ -basis modes.

Stability Analysis of Discrete-Time Semi-Markov Jump Linear Systems With Time Delay

Stability Analysis of Discrete-Time Semi-Markov Jump Linear Systems With Time Delay

Region stability analysis and precise tracking control of linear stochastic systems

This paper provides a novel region stability criterion on the basis of the pole (eigenvalue) distribution of the linear stochastic system (LSS). Corresponding stabilization control and tracking control are also discussed, which are more suitable for practical engineering applications. First, in the light of the connection between the eigenvalues of the system and the dynamic properties of LSSs, the concept of region stability is given to describe the finer dynamic behavior of LSSs. The criterion for the region stability is also presented. Second, the region stabilization method is investigated according to region stability, which can ensure that the system satisfies a certain dynamic performance by setting the eigenvalues in a certain convex region. Third, a precise tracking control method of LSSs is addressed as an application of region stabilization. It can regulate the steady state properties and transient response of the tracking signal more precisely. Two examples are given to demonstrate the effectiveness of the new methods.

Stability and passivity analysis of higher‐order differential systems inspired by RLC circuits

SummaryThis paper discusses the global asymptotic stability and strong passivity analysis of fourth‐order nonlinear and time‐varying dynamical systems by utilizing the Lyapunov direct method. The mathematical model of the main system is obtained from a non‐linear and aging RLC circuit that we have designed before. RLC circuits play an excellent role in the stability of modern system theory. Without the concept of storage elements, the construction of Lyapunov or energy functions for nonlinear and time‐varying systems may be difficult. Because of this, although there are many studies on the stability concept, but the subject has not been completed yet. Therefore, this study may present some mathematical technicalities to the Lyapunov stability with physical considerations. The Lyapunov functions obtained from RLC circuits are natural storage functions, and they satisfy the dissipation inequality. The theoretical stability results of the system are also discussed by Lyapunov's linearization method. The relationship between stability and passivity is also given. Meanwhile, we realized that linear system analysis is not a guaranteed way for determining the stability properties of a full system. Finally, the correctness and availability of the proposed approach are verified through simulation results.