App.xaml

<Application x:Class="EllipsePropertyChangeDemo.App"
             xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
             xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
             xmlns:local="clr-namespace:EllipsePropertyChangeDemo"
             StartupUri="MainWindow.xaml">
  <Application.Resources>
    <ResourceDictionary>
      <ResourceDictionary.MergedDictionaries>
        <ResourceDictionary Source="/EllipseStyle.xaml"/>
      </ResourceDictionary.MergedDictionaries>
    </ResourceDictionary>
  </Application.Resources>
</Application>

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using System;
using System.ComponentModel;
using System.Runtime.CompilerServices;
using System.Windows.Input;

namespace EllipsePropertyChangeDemo
{
  public class EllipseViewModel : ObservablePropertyChange, ICommand // DependencyObject
  {
    public bool _ServerConnected;

    public bool ServerConnected
    {
      get { return _ServerConnected; }
      set
      {
        if (_ServerConnected != value)
        {
          _ServerConnected = value;
          OnPropertyChanged();
        }
      }
    }

    public event EventHandler? CanExecuteChanged;

    public bool CanExecute(object? parameter) => true;

    public void Execute(object? parameter) => ServerConnected = !ServerConnected;
  }

  public class ObservablePropertyChange : INotifyPropertyChanged
  {
    public event PropertyChangedEventHandler PropertyChanged;

    internal void OnPropertyChanged([CallerMemberName] string propertyName = "")
    {
      PropertyChanged?.Invoke(this, new PropertyChangedEventArgs(propertyName));

    }
  }
}

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<UserControl x:Class="EllipsePropertyChangeDemo.EllipseControl"
                     xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
                     xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml" 
                     xmlns:local="clr-namespace:EllipsePropertyChangeDemo"             
                     HorizontalAlignment="Left" VerticalAlignment="Center" Width="40" Height="40">

  <Canvas HorizontalAlignment="Left" VerticalAlignment="Center" Height="35" Width="35" >
    <Ellipse x:Name="LED" Margin="7"  HorizontalAlignment="Left" VerticalAlignment="Center" Style="{DynamicResource StyleLED}"  />
  </Canvas>

</UserControl>

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using System.ComponentModel;
using System.Windows;
using System.Windows.Controls;

namespace EllipsePropertyChangeDemo
{
  /// <summary>
  /// Interaction logic for EllipseControl.xaml
  /// </summary>
  public partial class EllipseControl : UserControl
  {
    EllipseViewModel evm = new EllipseViewModel();

    public EllipseControl()
    {
      InitializeComponent();
      //this.DataContext = evm;
      //evm.PropertyChanged += UpdateLED;
    }

    private void UpdateLED(object sender, PropertyChangedEventArgs e)
    {
      if (e.Equals(true))
      {
        this.LED.Style = (Style)App.Current.FindResource("GreenLED");
      }
    }
  }
}

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<ResourceDictionary xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
                            xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
                            xmlns:local="clr-namespace:EllipsePropertyChangeDemo">
  <Style x:Key="GreenLED" TargetType="{x:Type Ellipse}">
    <Style.Setters>
      <Setter Property="Height" Value="20" />
      <Setter Property="Width" Value="20" />
      <Setter Property="Stroke" Value="DarkBlue" />
      <Setter Property="StrokeThickness" Value="1" />
      <Setter Property="Fill">
        <Setter.Value>
          <RadialGradientBrush Center="0.3,0.3" Opacity="1">
            <RadialGradientBrush.GradientStops>
              <GradientStop Color="LightGreen" Offset=".05"/>
              <GradientStop Color="Green" Offset=".95"/>
            </RadialGradientBrush.GradientStops>
          </RadialGradientBrush>
        </Setter.Value>
      </Setter>
    </Style.Setters>
  </Style>
  <Style x:Key="RedLED" TargetType="{x:Type Ellipse}">
    <Style.Setters>
      <Setter Property="Height" Value="20" />
      <Setter Property="Width" Value="20" />
      <Setter Property="Stroke" Value="DarkBlue" />
      <Setter Property="StrokeThickness" Value="1" />
      <Setter Property="Fill">
        <Setter.Value>
          <RadialGradientBrush Center="0.3,0.3" Opacity="1">
            <RadialGradientBrush.GradientStops>
              <GradientStop Color="LightSalmon" Offset=".05"/>
              <GradientStop Color="Red" Offset=".95"/>
            </RadialGradientBrush.GradientStops>
          </RadialGradientBrush>
        </Setter.Value>
      </Setter>
    </Style.Setters>
  </Style>
  <Style x:Key="StyleLED" TargetType="{x:Type Ellipse}" >
    <Setter Property="Height" Value="20" />
    <Setter Property="Width" Value="20" />
    <Setter Property="Stroke" Value="DarkBlue" />
    <Setter Property="StrokeThickness" Value="1" />
    <Setter Property="Fill">
      <Setter.Value>
        <RadialGradientBrush Center="0.3,0.3" Opacity="1">
          <RadialGradientBrush.GradientStops>
            <GradientStop Color="LightSalmon" Offset=".05"/>
            <GradientStop Color="Red" Offset=".95"/>
          </RadialGradientBrush.GradientStops>
        </RadialGradientBrush>
      </Setter.Value>
    </Setter>
    <Style.Triggers>
      <DataTrigger Binding="{Binding Path=ServerConnected}" Value="true">
        <Setter  Property="Fill">
          <Setter.Value>
            <RadialGradientBrush Center="0.3,0.3" Opacity="1">
              <RadialGradientBrush.GradientStops>
                <GradientStop Color="LightGreen" Offset=".05"/>
                <GradientStop Color="Green" Offset=".95"/>
              </RadialGradientBrush.GradientStops>
            </RadialGradientBrush>
          </Setter.Value>
        </Setter>
      </DataTrigger>
    </Style.Triggers>
  </Style>
</ResourceDictionary>

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<Window x:Class="EllipsePropertyChangeDemo.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
        xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
        xmlns:local="clr-namespace:EllipsePropertyChangeDemo"
        mc:Ignorable="d"
        Title="MainWindow" Height="150" Width="200">
  <Window.DataContext>
    <local:EllipseViewModel />
  </Window.DataContext>
  <StackPanel>
    <local:EllipseControl/>
    <Button Content="Change" Command="{Binding}" Width="100"/>
  </StackPanel>
</Window>

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using System.Windows;

namespace EllipsePropertyChangeDemo
{
  /// <summary>
  /// Interaction logic for MainWindow.xaml
  /// </summary>
  public partial class MainWindow : Window
  {
    public MainWindow()
    {
      InitializeComponent();
    }
  }
}