How to toggle mat-expansion-panel with button click?

In your html file:

<mat-expansion-panel [expanded]="panelOpenState">

    <mat-expansion-panel-header>
        <mat-panel-title>
            TITLE
        </mat-panel-title>
    </mat-expansion-panel-header>

    <p>BODY</p>
</mat-expansion-panel>

<button mat-raised-button (click)="togglePanel">TOGGLE</button>

In your TS file:

panelOpenState: boolean = false;

togglePanel() {
    this.panelOpenState = !this.panelOpenState
}

If you use *ngFor to generate the expansion panels:

<mat-expansion-panel [expanded]="isOpen" *ngFor="let d of data">
    <mat-expansion-panel-header>
        {{ d.header }}
    </mat-expansion-panel-header>
    <p>{{ d.content }}</p>
</mat-expansion-panel>

<button mat-raised-button (click)="togglePanel">TOGGLE</button>

If you press the button all of the expanded panels opens simultaneously.

To open only one panel with one button, add a "expanded" property to the data array for each element like this:

  data = [
    {id:1, header:'HEADER 1', content:'CONTENT 1', expanded: false},
    {id:2, header:'HEADER 2', content:'CONTENT 2', expanded: false},
    {id:3, header:'HEADER 3', content:'CONTENT 3', expanded: false},
    {id:4, header:'HEADER 4', content:'CONTENT 4', expanded: false},
  ]

Then in your template:

<mat-expansion-panel [(ngModel)]="d.expanded" 
    [expanded]="d.expanded" *ngFor="let d of data" ngDefaultControl>

    <mat-expansion-panel-header>
        <button (click)="toggle(d.expanded)">TOGGLE</button>
        {{ d.header }}
    </mat-expansion-panel-header>
    <p>{{ d.content }}</p>

</mat-expansion-panel>

And the method raised by the button click:

  toggle(expanded) {
    expanded = !expanded;
  }

<mat-expansion-panel [disabled]="true"
                     #mep="matExpansionPanel"
                     *ngFor="let foo of list">
  <mat-expansion-panel-header>
      <button (click)="mep.expanded = !mep.expanded">Toggle</button>
  </mat-expansion-panel-header>

  <p>Text</p>

</mat-expansion-panel>