General State-space Form Research Articles

Zero-modified count time series with Markovian intensities

This paper proposes a method for analyzing count time series with inflation or deflation of zeros. In particular, zero-modified Poisson and zero-modified negative binomial series with intensities generated by non-negative Markov sequences are studied in detail. Parameters of the model are estimated by the method of estimating equations which is facilitated by expressing the model in a generalized state space form. The latent intensities required for estimation are extracted using generalized Kalman filter. Applications of the proposed model and its estimation methods are illustrated using simulated and real data sets.

Discrete-Time, Linear Periodic Time-Varying System Norm Estimation Using Finite Time Horizon Transfer Operators

The norm is one of the fundamental concepts of linear algebra and functional analysis. The notion of the norm is often employed in engineering, e.g. in control engineering, where main application is calculating the norm of the transfer function. Unfortunately existing methods are applicable for systems that can be described using Laplace transform, i.e. linear time-invariant (LTI) systems. An operational equivalent of the transfer function for linear time-varying systems is transfer operator. The transfer operator defined for finite time horizon can be described by finite dimensional matrix. Although for infinite time horizon the operator is infinite dimensional. In the paper a method for norm estimation of transfer operator defined on infinite time horizon is proposed. The method is applicable for linear time-varying, discrete-time systems given in general state-space form. The method take advantage of the properties of the transfer operator norm on a finite time horizon. Theoretical considerations are complemented by numerical examples.

LMI-based sufficient conditions for robust stability and stabilization of LTI-fractional-order systems subjected to interval and polytopic uncertainties

In this paper, by introducing a new general state-space form for uncertain linear time-invariant fractional-order systems subjected to interval and polytopic uncertainties, two problems including robust stability analysis and robust stabilization of the presented systems are investigated. Subsequently, two sufficient conditions in terms of several linear matrix inequalities for the problems mentioned are concluded as two separate theorems. It is assumed that the fractional order [Formula: see text] is a known constant belonging to [Formula: see text]. Simulation results of two different numerical examples demonstrate that the provided sufficient conditions are applicable and effective for tackling robust stability and stabilization problems.

Discrete-Time, Linear Periodic Time-Varying System Norm Estimation Using Finite Time Horizon Transfer Operators

The norm is one of the fundamental concepts of linear algebra and functional analysis. The notion of the norm is often employed in engineering, e.g. in control engineering, where main application is calculating the norm of the transfer function. Unfortunately existing methods are applicable for systems that can be described using Laplace transform, i.e. linear time-invariant (LTI) systems. An operational equivalent of the transfer function for linear time-varying systems is transfer operator. The transfer operator defined for finite time horizon can be described by finite dimensional matrix. Although for infinite time horizon the operator is infinite dimensional. In the paper a method for norm estimation of transfer operator defined on infinite time horizon is proposed. The method is applicable for linear time-varying, discrete-time systems given in general state-space form. The method takes advantage of the properties of the transfer operator norm on a finite time horizon. Theoretical considerations are complemented by numerical examples.

Realization in Generalized State Space form for 2-D Polynomial System Matrices

In this paper, a direct realization procedure is presented that brings a general 2-D polynomial system matrix to generalized state space (GSS) form, such that all the relevant properties including the zero structure of the system matrix are retained. It is shown that the transformation linking the original 2-D polynomial system matrix with its associated GSS form is zero coprime system equivalence. The exact nature of the resulting system matrix in GSS form and the transformation involved are established.

Process dynamics: modeling, analysis, and simulation

I. PROCESS MODELING. 1. Introduction. Motivation. Models. Systems. Background of the Reader. How To Use This Textbook. Courses Where This Textbook Can Be Used. 2. Process Modeling. Background. Balance Equations. Material Balances. Constitutive Relationships. Material and Energy Balances. Distributes Parameter Systems. Dimensionless Models. Explicit Solutions to Dynamic Models. General Form of Dynamic Models. II. NUMERICAL TECHNIQUES. 3. Algebraic Equations. Notations. General Form for a Linear System of Equations. Nonlinear Functions of a Single Variable. MATLAB Routines for Solving Functions of a Single Variable. Multivariable Systems. MATLAB Routines for Systems of Nonlinear Algebraic Equations. 4. Numerical Integration. Background. Euler Integration. Runge-Kutta Integration. MATLAB Integration Routines. III. LINEAR SYSTEMS ANALYSIS. 5. Linearization of Nonlinear Models: The State-Space Formulation. State Space Models. Linearization of Nonlinear Models. Interpretation of Linearization. Solution of the Zero-Input Form. Solution of the General State-Space Form. MATLAB Routines step and initial. 6. Solving Linear nth Order ODE Models. Background. Solving Homogeneous, Linear ODEs with Constant Coefficients. Solving Nonhomogeneous, Linear ODEs with Constant Coefficients. Equations with Time-Varying Parameters. Routh Stability Criterion-Determining Stability Without Calculating Eigenvalues. 7. An Introduction to Laplace Transforms. Motivation. Definition of the Laplace Transform. Examples of Laplace Transforms. Final and Initial Value Theorems. Application Examples. Table of Laplace Transforms. 8. Transfer Function Analysis of First-Order Systems. Perspective. Responses of First-Order Systems. Examples of Self-Regulating Processes. Integrating Processes. Lead-Lag Models. 9. Transfer Function Analysis of Higher-Order Systems. Responses of Second-Order Systems. Second-Order Systems with Numerator Dynamics. The Effect of Pole-Zero Locations on System Step Responses. Pad Approximation for Deadtime. Converting the Transfer Function Model to State-Space Form. MATLAB Routines for Step and Impulse Response. 10. Matrix Transfer Functions. A Second-Order Example. The General Method. MATLAB Routine ss2tf. 11. Block Diagrams. Introduction to Block Diagrams. Block Diagrams of Systems in Series. Pole-Zero Cancellation. Systems in Series. Blocks in Parallel. Feedback and Recycle Systems. Routh Stability Criterion Applied to Transfer Functions. SIMULINK. 12. Linear Systems Summary. Background. Linear Boundary Value Problems. Review of Methods for Linear Initial Value Problems. Introduction to Discrete-Time Models. Parameter Estimation of Discrete Linear Systems. IV. NONLINEAR SYSTEMS ANALYSIS. 13. Phase-Plane Analysis. Background. Linear System Examples. Generalization of Phase-Plane Behavior. Nonlinear Systems. 14. Introduction Nonlinear Dynamics: A Case Study of the Quadratic Map. Background. A Simple Population Growth Model. A More Realistic Population Model. Cobweb Diagrams. Bifurcation and Orbit Diagrams. Stability of Fixed-Point Solutions. Cascade of Period-Doublings. Further Comments on Chaotic Behavior. 15. Bifurcation Behavior of Single ODE Systems. Motivation. Illustration of Bifurcation Behavior. Types of Bifurcations. 16. Bifurcation Behavior of Two-State Systems. Background. Single-Dimensional Bifurcations in the Phase-Plane. Limit Cycle Behavior. The Hopf Bifurcation. 17. Introduction to Chaos: The Lorenz Equations. Introduction. Background. The Lorenz Equations. Stability Analysis of the Lorenz Equations. Numerical Study of the Lorenz Equations. Chaos in Chemical Systems. Other Issues in Chaos. IV. REVIEW AND LEARNING MODULES. Module 1 Introduction to MATLAB. Module 2 Review of Matrix Algebra. Module 3 Linear Regression. Module 4 Introduction to SIMULINK. Module 5 Stirred Tank Heaters. Module 6 Absorption. Module 7 Isothermal Continuous Stirred Tank Chemical Reactors. Module 8 Biochemical Reactors. Module 9 Diabatic Continuous Stirred Tank Reactors. Module 10 Ideal Binary Distillation. Index.

Digital design of variable structure control systems

Reachability conditions are developed for discrete single-input-single-output variable structure control systems described by linear mathematical models in general state-space form to reach a switching function from anywhere in state space. Stability conditions of a sliding mode are investigated. A modified algorithm is proposed to simplify the design procedure. Practical application to a thermal process has been achieved by using the modified algorithm to show the potential for development and practical results are compared with those using the classical PID controller design.

Robust Identification Scheme in an Adaptive Track-Controller for Ships

We describe the method of parameter estimation used in an adaptive track controller for ships, which we developed for commercial production. The choice of the algorithm was dominated by two main requirements: the algorithm had to be robust against temporarily poor excitation of one of the model parts and its complexity was limited by the moderate computational capacity in our specific hardware environment. The system model consists of a part describing the low frequency ship motion and a high frequency disturbance model. The identification problem is in general state space form with some states not directly measurable. The standard linear model form can be recovered, if the states are assumed to be known. As an approximation they can be reconstructed with an observer. Instead of using the current parameter estimates for designing a suboptimal observer, we use certain fixed average parameter values. This results in a very simple structure of the estimation algorithm with stability properties that are more easily to investigate in practise. In particular the obtained separation of the two model parts allows to taylor their respective parameter tracking algorithms according to the different patterns of excitation.

Pole placement for singular systems

In this paper, we present a pole placement design for singular systems in polynomial fraction form. The design can also be used for the role placement of singular systems in generalized state space form, and requires no decomposition.