In this chapter, modern control theory represents the system dynamics as a set of coupled first-order differential equations in a set of internal variables, known as state variables, together with a set of algebraic equations that combine the state into physical output variables.The state-space representation of LTI systems surpasses several limitations of the classical methods that are mostly based on input-output descriptions. Moreover, the increase in the number of inputs, or outputs, does not affect the complexity of the state-space representations.

Chapter Contents:

• 7.1 Fundamentals
• 7.1.1 List of symbols
• 7.1.2 State space representation
• 7.1.2.1 State variables
• 7.1.2.2 Similarity transformation
• 7.1.2.3 Modal transformation
• 7.1.3 The Cayley-Hamilton theorem
• 7.1.4 Matrix exponential
• 7.1.5 Computation of the matrix exponential
• 7.1.5.1 Taylor series expansion
• 7.1.5.2 Diagonalization
• 7.1.5.3 Approximation based on the Cayley-Hamilton theorem
• 7.1.5.4 Laplace transform
• 7.1.6 Solution of the state-space equation
• 7.1.7 Controllability
• 7.1.7.1 State controllability
• 7.1.7.2 Output controllability
• 7.1.8 Observability
• 7.2 Solved problems
• 7.3 Proposed problems
• 7.4 State space analysis of continuous systems using computer packages
• 7.4.1 MATLAB
• 7.4.2 SCILAB
• 7.4.3 OCTAVE

Inspec keywords: continuous systems; control system analysis; algebra; state-space methods; differential equations; linear systems

Other keywords: control theory; algebraic equations; LTI systems; state-space analysis; linear time-invariant systems; input-output description; continuous systems; state-space representation; coupled first-order differential equations

Subjects: Algebra; Control system analysis and synthesis methods; Mathematical analysis; Linear control systems