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Let <em>Λ</em> be a topological space and let <em>F</em> be a multifunction from <em>[0,a]x[0,b]x(</em><em><strong>R</strong></em>^<em>n</em><em>)</em>^<em>4</em><em>xΛ</em> into <em><strong>R</strong></em>^<em>n</em>. In this paper we prove that, under suitable assumptions, the set of all <em>λ</em> in <em>Λ </em><span style="font-style: normal;">such that the partial differential inclusion is locally controllable around the origin of </span><em><strong>R</strong></em>^<em>n</em><span style="font-style: normal;"> at the point </span><em>(a,b)</em><span style="font-style: normal;"> (resp. </span><em><strong>R</strong></em>^<em>n</em><span style="font-style: normal;">-completely controllable) is open in </span><em>Λ</em><span style="font-style: normal;">. Next, we present an application to the study of two kinds of controllability for the distribuited parameter control process.</span>