TABLE OF CONTENTS State-space models provide a general and strong basis for dynamic modeling of various systems including switching converters. State-space models are useful to design the needed linear control loops, and can also be used to computer simulate the steady state, as well as the dynamic behavior, of the switching converter, fitted with the designed feedback control loops and subjected to external perturbations. Furthermore, statespace models are the basis for applying powerful nonlinear control methods such as sliding mode. State-space averaging and linearization provides an elegant solution for the application of widely known linear control techniques to most switching converters.
Consider a switching converter with sets of power semiconductor structures, each one with two different circuit configurations, according to the state of the respective semiconductors, and operating in the continuous mode of conduction. Supposing the power semiconductors as controlled ideal switches (zero on-state voltage drops, zero offstate currents, and instantaneous commutation between the onand off-states), the time ( t) behavior of the circuit, over period T, can be represented by the general form of the state-space model (34.1):
where x is the state vector, 
= d x/d t, u is the input or control vector, and A, B, C, D are respectively the dynamics (or state), the input, the output, and the direct transmission (or feedforward) matrices.
Since the power semiconductors will either be conducting or blocking, a time-dependent switching...
