# PeriodicSystems.jl

## Linear periodic time-varying systems

## Compatibility

Julia 1.7 and higher.

## About

`PeriodicSystems.jl`

is intended to be a collection of Julia functions for numerical computations related to periodic system representations in the continuous-time form

```
dx(t)/dt = A(t)x(t) + B(t)u(t) ,
y(t) = C(t)x(t) + D(t)u(t) ,
```

or in the discrete-time form

```
x(t+1) = A(t)x(t) + B(t)u(t) ,
y(t) = C(t)x(t) + D(t)u(t) ,
```

where `x(t)`

, `u(t)`

and `y(t)`

are the system state vector, system input vector and system output vector, respectively, and `t`

is the continuous or discrete time variable. The system matrices satisfy `A(t) = A(t+T)`

, `B(t) = B(t+T)`

, `C(t) = C(t+T)`

, `D(t) = D(t+T)`

, i.e., are periodic with period `T`

.

Many control applications are formulated as genuine periodic control problems as for example, satellite attitude control, helicopter forward flight control, orbital stabilization of underactuated systems, etc. Besides that, periodic systems represent a general framework to analyze and design multi-rate sampled-data systems.

The targeted functionality of this package is described in [1].

[1] A. Varga. A Periodic Systems Toolbox for Matlab. Proc. of IFAC 2005 World Congress, Prague, Czech Republic, 2005.