State Space Representation

Then we represent the differential equation in state space in phase variable form.

State space representation. State space representation mathematical background and state of the art. The state space formulation of a set of differential equations is easier to solve with a digital computer. Converting from state space form to a transfer function is straightforward because the transfer function form is unique. State space representation advantages the state space concept simplifies the mathematical notation by the use of vector equations.

The state space model of linear time invariant lti system can be represented as x ax bu y cx du the first and the second equations are known as state equation and output equation respectively. The state space representation of a. To convert a transfer function into state equations in phase variable form we first convert the transfer function to a differential equation by cross multiplying and taking the inverse laplace transform assuming zero initial conditions. The resulting models 1.

Al kandari ph d in electrical. The state variables define the values of the output variables. Soliman abdel hady soliman ph d ahmad m. Make it easier to handle missing values measurement error.

Variablesiswrittenasastate vector x t x1 t x2 t xn t t andthesetof rinputs iswrittenasaninputvectoru t u1 t u2 t ur t t. A state space model is a mathematical representation of a physical system as a set of input output and state variables related by first order differential equations. Process tomography and estimation of velocity fields. The state space formulation is applicable to both linear and.

The state is observed directly and only partially observable via the observed data. The state space representation of a system is a common and extremely powerful method of representing a system mathematically. The ss model object can represent siso or mimo state space models in continuous time or discrete time. This page only discusses how to develop the state space representation the solution of state space problems are discussed elsewhere.

State space models the data is a linear function of an underlying markov process the state plus additive noise. Two of the most powerful and common ways to represent systems are the transfer function form and the state space form. This form of the state equations explicitly represents the basic elements contained in thedefinitionofastatedeterminedsystem.